Texas, must be a nice place
Nearly all the rest of the country considers a .223 to be a varmint round, and not suitable for deer. While virtually any bullet will kill, sport hunting should be done with rounds that will do the job humanely.
Using the .223 for deer (where legal) requires both pin point accuracy, AND proper bullet selection. I use the .223 for varmints, using bullets in the 52gr-55gr range. These bullets are designed to expand violently when they encounter minimal resistance. A twig, or even a blade of grass can cause them to "blow up" These bullets are not at all suitable for deer hunting, they lack the penetration needed to reach vital organs. They are capable of creating a massive surface wound, which is not a good thing, being both inhumane, and damaging to the meat.
Heavier bullets are constructed for more penetration, but here you run into a couple of problems. One is that some of these bullets are intended for target use, and the other is the loss of velocity, particularly at extended ranges. Putting a .22 caliber hole in a deer will kill humanely, only if the shot is perfect. And perfect shots at extended ranges are on the tough side of difficult. Mostly because of wind drift.
Back when the Army issued me an M16A1, they said the max range of the 5.56mm was 460 meters, and we only shot to distances of 300 meters. Here's something to think about, using the GI 55gr bullet (not legal for hunting) for comparison, by the time it gets to 600 meters, it has the energy of a .22LR at the muzzle. Even though heavier bullets will retain energy better, this is still not a good idea for deer, even the small Texas ones.
Now the .25-06 is a different thing altogether. It will launch a bullet weighing nearly twice that of a .223, at nearly the same speed. This translates into a much higher amount of retained energy at long range, more than enough for humane kills. The .25-06 does this with a much larger case, holding nearly twice the amount of powder, and so has a greater blast and recoil than the .223. It also has the advantage of being legal for deer hunting all over the country (where ever rifles are allowed).
The ranges you state you plan to shoot at would be considered ridiculous by everyone I know, but if you are good enough to make those shots, well, perhaps you ought to be shooting competitively.
I have always felt that if you couldn't get within 300 yards of a game animal (or less), you should write yourself a letter explaning why you had to shoot at such a long distance. In triplicate. Now, shooting varmints is another matter. The sport in varmint hunting is making the long shot, not stalking close as it is with deer. I grew up hunting deer in the north woods, and woodchucks in the open fields. And that is my personal basis for defining "sport". Is it different in Texas?