I concur that there are out of state girls in every house at UT, so it is very attainable.
You have started at a great time to get your ducks in a row for recruitment. Start working on getting your recs now.
From the recs I have done for UT girls, they want 1 formal rec (the form that is downloaded from the sorority website) and 3 letters of support (including the formal rec writer), then 2 pics, one a face shot and one a 3/4, these do NOT have to be formal studio type, your mom can take pics of you outside (and a snowy picture might be a real standout

).
I also agree that it is a good idea to google some of the Texas panhellenic websites, Houston has one, Katy has one, Richardson is named above, etc. They all have "how to's" that have information about clothing choices, accessories, etc. AND, peruse the threads on GC about "what to do" and Texas Recruitment, there is a TON of good information.
DO NOT let it intimidate you! You are obviously a smart girl or you wouldn't have been accepted this early at UT - you have to be a top oos (no brainer) admit. So, now that you're in, start working on the other stuff.
You will meet a bunch of girls when you come down for orientation week in the summer. Try to get to know other girls who are rushing, they might give you in's with girls they know in houses.
There is a house for every type of girl (who wants to be Greek) at UT. Give it a chance and best of luck to you!! If you want to ask anything else, please feel free to do so. I don't have a daughter at UT, I have a sophomore son, but I have been writitng UT recs for 20 years and I know many wonderful young women there in many different houses.
*I agree that being from the midwest might be a good thing, it makes you different!