Without reading everything that's been said yet, here's what I got to say:
The Texas Reenacting Scene:
You won't find a great number of reenactments in Texas, and the just about all of them you'll have to drive a ways. Coming up on October 14-16th is the mainstream event in Mexia, TX at the Confederate Reunion Grounds. Its an event that fell on hard times and there's a max effort this year to keep it going. After that there's no events in Texas I can think of till next Spring, with that one being Jefferson, TX. Its an event with TWO reenactments that compete in the same month, but I can tell you working with the landowner at one next May might be good and it'll probably get better. There's the before mentioned TMVI incompetency, but I'm sure they'll shoot themselves in the foot next year. Again...
Where the events really be out here:
Due to no CW Battles here of note that can be reenacted, you can't find many in Texas. There used to be more of them, all made up, but no more. You'll have to go to Louisiana, Arkansas, and Oklahoma for the closest ones formal reenactment wise. On November 5th and 6th there will be one in Old Washington, Arkansas, which is just on the other side of Texarkana, so while a 5 or 6 hour drive from you, it's right by Texas at least! This event, like most all left in Texas is made up, but its a State Park with many, many historic structures and served as Arkansas' State Capitol after the Fall of Little Rock. Even the "capitol" is still there preserved. Its an event that died and is being brought back and if it goes like it used to, I highly recommend it as a starter event.
After that for this year, there's the 160th Anniversary Battle of Prairie Grove up by the Missouri Border at Fayetteville, which may be too long a drive just starting out.
Next year, near Donaldsonville, Louisiana in February at the site of Fort Beauregard, which had a Naval duel in the war, a reenactment, then in April is the Battle of Pleasant Hill near Mansfield. "P. Hill" as its commonly known, I can't comment on it too much these days. It used to be my top favorite event, but the numbskulls in power refusing to retire or just die off and get out the way, with non-historically minded people holding the purse strings, ran that event so far into the ground I swore it off till they straighten their act up in 2015. But I'd still say its good place to go for a newbie. You'll get to see how its been reenacted for the past 30 years with no regard to history of that battle.
Getting started:
If you PM me, I can put you in contact with the people you should talk to. If your wanting to go hardcore stitchcounter, and younger in age, I can put you in contact with a man in "The Invincibles" out on the other side of Mason at Fort McKavett and he'll do you right on getting started out. They even do "living histories" out there which are very, very strict in regard to historical accuracy. This is a very big problem just starting out, as a lot campaigners demand a separate bit of kit for every event, and the costs go up with a big amount of money need to buy a whole new kit every time there's an event, depending on what time in history, even separate kit for the same event. But hey its close to you!
If you just wanna get your feet wet first, and can on such short notice, you can go to Mexia and I'll make some calls and get you in contact with my unit, and some loaner gear might can be made available, and you can burn some powder. Plus, you'll probably have to listen to folks in 1880's and 1890's cowboy era cloths tell you how I'm an arrogant a**hole that doesn't know anything about CW soldiers, gear, and uniforms because I'm not over 50 more or less.

(hint, hint about TMVI units...)
Now if my work doesn't have other ideas, you can PM me and I plan on being at Old Washington and I'll loan you a musket and get you started as best as I can with others on uniforms and gear.
Costs...
THIS IS NOT A CHEAP HOBBY!!!!!!! It'll be costly. You can buy cheap foreign made junk that looks nothing like what they had and will either fall apart and roast you alive in 30-degree weather.
You do not, ever under any circumstances go out and buy stuff on your own starting out. You will regret it. It may sound harsh, but I say this for your own good. If you got the coin, and can make Old Washington, I'll guide you at the sutlers on good stuff, and what not to buy, and can even online tell you the best places to go. I would be able to make you some stuff myself at cost like I've done for others, but I don't have time to do so for even myself anymore.
You will not ever just go one side, you'll always do both blue and gray, frequently on the same weekend with normal or "mainstream" events around here, so you really have to have two kits of stuff at the very least.
Now after that long word fit, I can promise if you like campfires, sleeping on the ground, or even in a tent, you will have fun and enjoy it. I've no idea your age and so forth, but this hobby is better for the younger and fitter than older. PM if you got questions and wanna get started.
And finally, if you ain't noticed by what I've said, I would say "stitch-counters" ain't really a big worry. Some are a royal pain that I'd literally laugh if they were on fire, others like who've I've spoken of are hands down the best folks I've ever known or known of. You'll find reenactors of
every stripe are a very, very mixed bag of good and agonizingly bad. Its just a question of who you associate with.
Also, last word for real this time, STAY AWAY FROM THE DISMOUNTED CAVALRY!!!!!!!!! For your own safety!