Caliber Suggestions?

[Varmint Hunter]

Based on your criteria I'd opt for the 260 Rem even though it wasn't on your list. At 300 yds it would certainly have more bang-flop than the other cartridges and recoil would still be quite manageable.
Just my 2 cents.

 

[Randominator]

Out of the calibers you have listed, my first choice would be the 6mm BR. I have a 15" Encore barrel in this caliber and it will cleanly take deer size animals out to 300 yards.

I shoot 100 grain Nosler's at 2610 fps. I shot a group Sunday with this load at 200 yards that measured .960".

I load 75 grain V-Max's for use on varmints. 2941 fps. and .535" at 100 yards.

I have been shooting the 6mm BR since 2006 and I'm still using the 100 pieces of Lapua brass I bought with the barrel. There are usually blemished bullets for sale in 6mm on Nosler's Shooters Pro Shop.

 

[Unofficial Gun Addict (UGA)]

Since others have made suggestions not on your list... Well.. I'm gonna chime in too on that side of the fence. For long range pistol in light recoiling round... I'd go with the 7mm-08. Tons of powder, bullet, and brass out there, can load hotter or tamer depending on your tastes, and 7mm BC is bout the best you'll find. Some may argue the 6.5, but with you wanting deer, you never know when you might go for elk, and the 7mm will allow you to bump up to heavier bullets more than capable of the task.

Good luck and hope you have lots of fun making your decision... and more fun bagging deer.