Given you're in TX and didn't express any interest in elk /moose/big bears (which your .308 could handle anyway, although it wouldn't be my first choice)....
You've got varmints pretty well covered with the .22-250 and deer and pigs with the .308. I prefer the .257 Roberts and .25-06 to a .243. Since you already have a .25-06 pistol a rifle in that caliber makes some sense. The .257 Roberts is a better cartridge for handloaders who can use +P data and really take advantage of its capabilities. Going up a bit in caliber it's hard to go wrong with a 7mm-08, either.
That said, I'm going to suggest something entirely different - something fun and relatively inexpensive to shoot. I know this is a bolt gun forum but my suggestion would be to look at lever guns. I shoot both bolt guns and lever guns and the lever guns have always registered higher on the FUN scale. A Marlin in .357 Mag or .44 Mag will provide hours of shooting fun at minimal cost and recoil is very mild. Although I shoot my Browniing B92 .44 MAg at 200 ayrds on a regular basis, its useful hunting range is best limited to 100-125 yards and I would limit a .357 Mag even more.. A step up in power, recoil and ammo cost is the .30-30, which is fine out to 200 yards (1,000fpe for a 150g bullet) for deer. Ammo, while more expensive, is still relatively cheap at around $12 a box of 20. One more step up is the 450 Marlin and .45-70. Recoil on factory 450s is probably more than you want, and ammo selection for the 450 is limited, but the .45-70 offers a very wide range of ammo from cheap and mild cowboy loads you can shoot all day to ammo that can (and has) taken Africas Big Seven. Cowboy ammo runs about $12 a box, normal ammo will run $18-$22 a box and premium hunting ammo like that from Garrett and Buffalo Bore will run $40-$60 per box of 20. If your pocket book can stand it, Garrett offers loads that use Speers 500 grain African Grand Slam Tungsten Solid for only $180 a box. One of my favorite loads (as a reloader) is 300 grain hardcast over 13.5 grains HS-6. Velocity is around 1100fps and ammo costs me $2.50 per box. Recoil for these loads is about half that of factory .30-30 loads.
The only caution about lever guns is that they are rather addicting. Like a lot of other bolt-gun shooters, I started out with one but somehow they proliferated - to the point where I have a Browning B92 in .44 Mag and Marlins in .30-30, .375Win and .45-70. The last three big game animals Ive taken (buck antelope with the .375Win, forkhorn mulie and 6x6 bull elk with the .45-70) were taken with the leverguns. When the girls go shooting with me we take the .30-30 and .45-70, and they prefer the .45-70 with the plinker loads. When I want to blow up a row of water jugs I reach for the .45-70 and hardcast hunting loads. When I want to wrap the swinging steel gongs around the pole they are supported from I again reach for the .45-70 and heavy hardcast. For clay pigeons at 200 yards its the .30-30. Like I said, addicting...