For the longer barrel life I'd look at either a 243Win. or 6mm Rem. The 6mmRem. might
have just a very slight edge on the 243Win., but as you will be handloading the difference would be negligible. Though the 25-06 can be an excellent varmint rifle I suspect it would burn out a barrel a lot quicker than either of the 6mm cartridges. It also has substantially more recoil. Not a fun gun to shoot if you find yourself with an afternoon to kill in a priairie dog town. Personally, I'd go for the 243Win. I think it's probably the most accurate of the three also. Many a dog came to an end of his trail when I used one in Wyoming.
For varmint rifles I'd look at either the Ruger varmint rifle with laminated stock, or one of the stainless Remingtons with synthetic stk.
BTW, if you go for the 243Win., a bullet I found to shoot really good was the Sierra
85gr. BTHP. Half inch groups ( 5 shots ) were the norm. Nice too, this bullet is available
in a Federal Premium loading if you need to pick up a box.

ps: Welcome to the forum!