Tman --- 621 acres, man that's a real nice sized place for a beginner, I'd kinda like to be in your shoes!
Try to get yourself a good, experienced local mentor, preferably a guy that actually makes his living ranching in south Texas. Also, study all you can about the different breeds of cattle common in your area and have a look at all the publications that A & M has to offer on forages, drought mgmt., cattle diseases, management, etc. If you decide to try to buy some more cattle at one of the good replacement auctions try to take a well experienced cattleman with you and follow his lead and advice. And don't be afraid to sit there with your hands under your butt, so to speak, because you don't need to buy all your cattle (or any, for that matter) your first time out --- and some auctioneers are more than happy to take extreme advantgage of a newbie. Don't try to buy your herd at a normal weekday auction. Don't try to cut corners and go the cheapie route when it comes to buying your bulls. In south Texas you'll see a lot of what are called "tigerstripe" cows (50/50 Brahman/Hereford crosses) and unless you just overpay you really can't go too wrong buying them. Being a newbie, I would recommend that you not put Charolais bulls with any first or second calf heifers because of possible calving problems. A Brangus bull would be fine to use IMHO.
Get an experienced person to assess and advise you on the condition and adequacy of your fencing (including cross fencing), corrals, catch trap, water sources, etc. Learn about rotational grazing and the proper fertilization requirements for your bermuda pastures. Decide what you intend to do about winter feeding, hay buying, stockpiling of forage, etc. Start a maintenance program on the mesquite --- you probably can't completely eradicate it but you need to very much control it before it really takes over.
You might also consider leasing some of your place to a trusted and experienced cattleman as a way of letting yourself ease into the business and being able to closely observe and learn from somebody else (with a properly written and well thought out lease agreement).
With a place full or bermuda you probably don't have much in the way of deer do you? As you probably know deer/quail/dove hunting revenue is typically a MAJOR component of ranching revenues in south Texas and for many ranchers wildlife mgmt. is a very important ranching consideration.
Man, there are so many things to consider and I could ramble on and on so I'll stop now. Don't be afraid to ask questions here, and of the ranchers in your locale. If you can, learn from the mistakes of others rather than from your own!
Good luck, Arnold Ziffle