Renee is going to be the expert on Texas.
This is a quick generalized overview of some things......
Right now I can guarantee you that one thing you won't go wrong with is to take the online NIMS classes ICS 100,200,700,800,809 - They are free. Take the classes and print the certificates (actually I would print them to PDF files and keep them as you will be asked for them for many activities and future certifications)
Emergency Management Institute - FEMA Independent Study Program
Basically there is wilderness and disaster SAR and you have not specified which. Are you looking at K9 SAR as a volunteer, at a search and rescue career in some department (most of which is not dogs) etc. The typcial K9 volunteer on a wilderness team looking for individiual lost people (kids, nursing home walkaways, hunters, etc). Disaster training is specialized enough that only a handful of teams across the country do it. and travel for callouts.
Most training is done in conjunction with an organized team and not through independant classes or training centers (at least for typical wilderness SAR)
I can only speak to being a wilderness volunteer though others can to the disaster disciplines. Typically the training is specified by the individual team but good background things (in addition to NIMS) are
NASAR FUNSAR SAR III, SAR II - www.nasar.org
(if money is tight, wait before you do this)
First aid and CPR, adult and children. Never hurts to have higher levels of training such as DOT First REsponder - BUT - a typical SAR team member is not providing medical aid, however it is good to have this for training with your teammates where someone may get hurt during training or on a search.
HAZMAT, Bloodborne pathogens. Once again - the SAR team will provide training opportunities
Crime Scene Presevation (only valid if taught by law enforcement)