The Winchester Model 70 featherweight is an excellent (classic beauty)gun and 243 is an excellent choice for Texas deer. The 243 is versatile and very capable for Texas size deer and allow you to kill a lot of smaller (or larger for that matter) game.
A 308 or 30-06 is ridiculous for deer. Moose, brown bear, etc, sure, deer not needed. there are probably 10 or 20 other workable choices that we all could pimp. I dont have a 243, and make do with 7mm-08. But is not better, it is just what I happen to have. If I lost my 7mm-08 I would personally look at one of the 6.5mm like the 260 Rem or the Sweed, but really it is all about the same. The 6.5 might go a little longer without the recoil penalty of some of the other suggestions.
A 308 or 30-06 is ridiculous for deer. Moose, brown bear, etc, sure, deer not needed. there are probably 10 or 20 other workable choices that we all could pimp. I dont have a 243, and make do with 7mm-08. But is not better, it is just what I happen to have. If I lost my 7mm-08 I would personally look at one of the 6.5mm like the 260 Rem or the Sweed, but really it is all about the same. The 6.5 might go a little longer without the recoil penalty of some of the other suggestions.