My first deer rifle was a .243 Winchester. I still have it and have shot lots of deer with it. All one shot kills. And I had a friend in Montana (he passed on) who used a .243 on elk, but he was able to get relatively close and place his shots. Having said that, if you're talking only one rifle for both deer and hogs, I would look at a .308 Winchester. A little easier on recoil than a .30-06 and cartridges with varying bullet weights and styles are available. The .308 will do pretty much anything a .30-06 will do with less powder.
I'm a big fan of Savage bolt actions. Excellent rifle with an inexpensive price compared to Remington and Winchester models.
There's no one perfect cartridge. I've used .223, .22-250, .243 and .30-06. I've had animals run with all four even with the .30-06 and hit was a perfect hit right through the vitals( heart and lungs were toast ). So I think it just depends on what the shooter wants personally. But keep in mind the smaller the caliber the less forgiving it is about shoot placement.
Agree, but if this is your first rifle & your wife is also going to shoot it, then IMHO the .243 is the way to start off with. If it's just you that's going to do the shooting, then I recommend the Win. 270 (in any name brand).
Given the lack of more specific information - and probably even with more info: Savage or Tikka in 25-06. Low to medium price, both accurate out of the box, 25-06 will drop anything you're likely to run into in Texas, and most other places as well.
My wife loved taking hogs & deer with her brothers .243. When it was time for her own rifle, she went with the 25-06. Either of those are great starters and either will kill anything native to Texas. We know a lady that shoots a 30-06, but it does have more kick. I think it's easier to learn on something that doesn't intimidate you with its recoil. Due to that reason alone, I'd start with .243 or 25-06.