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"Texas has yet to learn submission to any oppression, come from what source it may." - Sam Houston, first President of Texas
Texas is a fledgling nation during the starting time of Victoria 2, in the middle of the war for its independence against Mexico. While losing most battles, including the massacres at Goliad and The Alamo, the young state scored a decisive victory at the Battle of San Jacinto, capturing the Mexican President and Dictator General Antonio López de Santa Anna.
The Texan economy starts in pretty poor shape, with no industry to speak of and an extremely low population. As of the latest patch, an event occurs early in the game in which Texas overruns Mexican garrisons, giving them extra supplies and a lump sum of money, allowing you to run without a deficit for a time while fully supplying your armies.
If you can, try and get the nationalist party in power by holding more elections -- not so much for the State Capitalism aspect, but simply so you can set taxes high enough to offset the supply cost when you run out. You still won't be able to run in the green, even with maxed out taxes and tariffs, but it will help delay bankruptcy and reduce the debt you'll run up if the war with Mexico continues for too long.
Texas starts with the first rank of every technology group, save for Experimental Railroads, and a Traditional Academia. Depending on your goal throughout the game, different technologies will be useful to you. If you're planning on applying for statehood or remaining a secondary power to gain the benefit of being in the American Sphere of Influence, you'll probably find Stock Exchange or Ad-hoc Money Bill Printing under Commerce to be very useful, as both increase Tax Efficiency (Stock Exchange directly so, Money Bill Printing through inventions.).
If you're angling for Great Power status, getting Romanticism then Idealism first is very important, as it allows for the biggest potential gains in prestige for your tiny nation at the start of the game. Interestingly enough, Ideological thought, after Idealism, will give a large boost to your research efforts through boosting the plurality of your nation (By inventions, that is.).
The Power section in the Industry tree of technology will give a boost to your cattle production, which makes a big difference to your resource output, since all but one of your territories benefit from it. Eventually, however, you'll need to develop your military tree, of which you should consider the army leadership section to have priority (It helps to preserve your small population of soldiers, very useful for a population poor nation.), followed by light and heavy armaments.
The Texan parties all have different benefits to having each in power, although as a democracy, it can be tricky to dictate which will rule. All three starting parties support Residency.
Liberal: The Democratic Party
The Democratic Party is probably the easiest to keep in power, and works well for enacting political reforms, while still being Jingoistic, allowing the Texan player strong military growth. The policy of Free Trade, however, can create difficulties in using tariffs to supplement treasury shortfalls, however, and Laissez Faire will forbid the government from opening or supporting factories.
Conservative: The Whigs
The Whigs favor industrialism and commerce over war and to that end is the first available non-jingoistic choice for Texas, being Anti Military. Like the Democratic Party, the Whigs support Laissez Faire policies, but also favor Protectionism over Free Trade.
Nationalist: The Nationalist Party
The main benefit of The Nationalist Party is the State Capitalism aspect; with nationalists in power, it will be much easier to open and support factories that produce military and other useful goods for your nation, highly recommended for those looking to achieve Great Power status. Coupled with Jingoism and Protectionism, you'll be able to raise a large army and fund it with the help of tariffs.
Anarcho-Liberal: The Radical Party
Later, the Radical Party will become available, which holds two major differences from The Democratic Party -- A policy of pacifism, and a policy of Full Citizenship.
The Texan Revolution
Texas has a few strategic paths available to it, but first things first; you need to take back your land from Mexico.
This can be easy or hard, depending on how willing you are to gamble with the fate of your nation. For the easiest of strategies, simply allow Mexican forces to take part of your land, or defeat your army, which will allow the United States to intervene. Usually after US intervention, Mexico will offer white peace in the face of the superior army. After this, you'll be left to pick up the pieces of a defensive war, not to mention you'll only have five territories to work with.
To obtain the historically correct borders of Texas, you'll need to go on the offensive. Not only is your army about 1/3 of the size of the Mexican invasion force, your stockpile of resources also puts you on a time limit; if you can't achieve victory before your stockpile is depleted, you'll spiral downward into debt, meaning even with victory you'll have a hard time getting back up. Not to mention, your tiny population will bar you from being able to recruit, or even reinforce, soldiers. To your benefit, however, General Sam Houston is a master of defense, providing a whopping 6 (!) to defense. I have seen the full weight of the Mexican army defeated when they attack a dug in Sam Houston, quite amazing, I must say. Because of this, the AI is very reluctant to attack you.
When you start out, if you're planning to acquire Mexican Texas, make a beeline for Laredo. Santa Ana, the Mexican president and general, leads a small force which will usually arrive in San Antonio before making a retreat from your approaching army. When you arrive in Laredo, the rest of the Mexican regulars will arrive and tend to gather at Reynosa -- after that, as long as you have soldiers adjacent to them, they simply won't move. Use this opportunity to split off the cavalry regiment from your main army and take El Paso, which is greatly needed for forcing peace without American intervention, as it reduces the cost of the "Acquire Mexican Texas" wargoal to only 5 points. From here, dance your armies around the dug in Mexican force, taking as many towns around them as you can; your Guard/Artillery force should take Matamoros and Monterrey, then merge with your cavalry regiment and make a beeline for Mexico City. That's right; you're going to move on the Mexican capital with your tiny force. A bold move.
After you move away from the Mexican army, they'll begin to split up and retake the territory you've gained, but usually when you arrive in Mexico City, they'll agree to peace in exchange for you not sacking their capital. Sometimes, however, you'll need to wait until you capture it, which can sometimes cut close to you going bankrupt (By now, you'll be out of supplies and be forced to take loans to keep fighting.). After all this, you should acquire the full Republic of Texas sans a portion of New Mexico and Colorado (The Republic of Texas actually held these lands as well, although they had little to no development in them.).
At this point, you should be able to start building your population. If you're looking to simply hold on to Texan lands, rather than expand, set your national focus to either "Encourage Bureaucrats" to help increase tariff taxes or "Attract Immigrants" to simply increase your population. If the United States hasn't started yet, and you're a secondary power, you can also colonize Oklahoma; doing so will give you all the benefits of a second region, which is required to become a Great Power (Great Powers require that you have more than one region under your control, no exceptions.).
Work on balancing your budget by increasing tax revenue. As stated earlier, the first two sections in the commerce tree can help improve your tax efficiency, which at this point will greatly increase your income. Increasing your administrative efficiency by "Encouraging Bureaucrats" will increase the money you get from tariffs. At some point, you should look into "Encouraging Clergy" to boost your research; getting technology faster is key to the improvement of your nation.
Keep in mind your ultimate goals as Texas. Do you want to apply for statehood when you can? Would you like to remain independent, yet benefit from the US sphere of influence to protect your small nation? Are you intent on becoming a Great Power?
Applying for Statehood
If your end goal is to apply for statehood, then mostly, things are pretty set for you; build your reputation with the USA, then enact the decision. Doing so will end the game for you. A thing to consider, however, if you plan to join the CSA later in the game, you'll want to build your economy and military up as much as you can beforehand. The CSA usually tends to start in a weak position from what I've seen in game, and a powerful Texan state will greatly aid them in their defense. (Note: Texas applied for statehood in 1845, for those of you who want to keep history somewhat accurate.)
To have an easier time in the game, if you remain a single territory nation, you'll be prevented from becoming a great power, no matter how strong your nation becomes. This can be to your benefit, as the US will keep you in their sphere, which hurts your ability to conduct trade, but instead gives you a powerful ally. It also creates strange situations where Texas may be ranked in the top eight nations of the world, yet still be a secondary power. From this position, you'll usually act as a wildcard in fights, allowing you to determine the winner in conflicts, but never actually start wars yourself. Keep your reputation with the USA high, however; eventually, they'll gain cores on all your territory, and start eying your land real hard...
If you're set on becoming a great power, you've got a long road ahead of you. If you can't acquire Oklahoma before the US, the only other choice you'll have is to attempt to take an island from another nation. Haiti is easy to fight, but is usually in the US sphere of influence by this time; Cuba will probably be your only option, which will require considerable strength to wrest from Spanish control. You'll need a powerful navy if you've got your sights set on it.
Mexico will usually be off limits if you've acquired Mexican Texas without USA's aid -- the USA will usually choose to ally with them! The good news is that they'll usually ally with you as well once you're in their sphere, and when you become a great power, they'll usually keep their alliance until you break it. Just be careful not to call them to any offensive wars after you reach great power status; they'll always decline, breaking the alliance, and thus allowing them to declare war on you.
From here, the rest of the game is up to you. Have fun!