Bryan,
Your wife can file in TX, as long as she has lived in Tx for at least six months prior to filing, and three months (90 days) in the county in which she files.
You can sign a waiver, instead of having the Court, or a private process server company serve you with the Citation and Petition.
If you are both savy, you may, both, be able to do the divorce, pro se (representing yourself). Some attorneys may review your docs for you, and advise you as to property division, child support and medical support (both calculation and necessary wording in your Divorce Decree). Attorneys who advertise as "Collaborative Law' specialize in that (but be careful of the rates, & any Family Law attorney can do this, also).
Be careful of attorneys who advertise fifteen areas of expertise: Family Law, Criminal Law, Bankruptcy, Estate Planning, etc. You want someone who knows Family Law very well, and can pound out your Pleadings in half an hour, not someone you're paying to learn how to do them.
Only Mom has to appear in Court, if there is an Agreed Divorce (both of you sign the Divorce Decree). Some Judges don't require a court appearance by either spouse, if there is an agreed (signed by both) Divorce Decree. (If Mom has to appear, it's usually just to recite jurisdictional facts, and info re dates, children, support on the record - a brief appearance).
Tx requires a minimum 60 day wait, after filing of the Petition, before a Divorce can be granted (use 61 days to set the final hearing).
You both have to wait 30 days after the Judge grants the Divorce, before either of you can remarry (you can ask for a waiver of the waiting period, but that may require a court appearance for that purpose).
Be careful of attorney charges - they vary greatly on uncontested divorces. Also be aware - if you hire an attorney, make sure the fee agreement includes court appearance and attorney being the attorney of record on the pleadings. Some attorneys advertise very low 'uncontested divorce' rates, but they only do the paperwork and fill it out with the party as pro se - they don't appear in court, and they don't follow the case to ensure all is filed properly and set the hearing, etc.
IMHO, a reasonable rate for an uncontested divorce with c/s, m/s, and little community property, shouldn't be more than $600, with an additional $250 for court filing fees - $850. total. But, that is just my humble opinion.
(Prices vary according to area, but it shouldn't be much higher, and you can find lower prices). Your wife should call various family law attorneys in her county and price 'uncontested divorces'.
She should be sure to note what services are being offered by the attorney, so she can compare them: complete attorney representation (attorney is the 'attorney of record', the attorney will do the Petition, a waiver for you to sign (watch the wording - you want notice of all hearings, and only proceed with your signature on the agreement, or hearing with distribution by Judge. You're not waiving notice of future hearings, or allowing wife to proceed without your participation), possibly an Agreement Incident to Divorce, and an Agreed Divorce Decree.
Your waiver should include the statement that you are active duty military, and are waiving your rights under the Servicepersons Civil Relief Act.
There are a few publications regarding 'Do Your Own Tx Divorce'. Even if you are going to hire an attorney, it is a good idea to purchase or read one of these books to better understand the process and what the Court needs from the parties.
It is, always, advisable to hire an attorney. However, for some people, it's just not an available option. Be careful that you understand what you are signing (both present and future impact).
If you can't afford to hire an attorney to fully represent you, it is advisable to pay a Tx attorney for a few hours to go over your paperwork or advise you regarding the process - they can do that by email or phone (email is better - you can refer to email later). Also, many courts allow a telephonic appearance by out-of-state litigants.
Good luck.