Since you want to shoot alot (volume) of target shooting with the rifle, you will be VERY disappointed in any caliber and cartridge if you buy a thin light hunting/sporter barrel. Hunting/sporter barrels heat up too fast and then start to string shots wildly out of the group. In warm weather it seems to take forever for a sporter barrel to cool, and then 3 to 5 shots later its so hot again you can't keep your hand on it (egg frying hot). Bring a book to the range because you will need it to pass the time for barrel cooling time between 5 shot groups. 95% of your time will be just sitting there waiting for barrel cooling. If there are shooters waiting for a bench, you won't look good occupying a bench and reading a book!
For target shooting I recommend a heavy varmint type barrel, or straight 1.25" barrel. These absorb heat very well and extend the number of rounds you can shoot before time for cooling. In cold weather you can shoot indefinitely if you slow the pace down enough for the air to cool it. Placing a battery powered fan on the bench beside it, or using the internal barrel cooler fans, will help alot. I use both.
Heavy varmint and straight barrels are very heavy and you will not want to carry them for hunting, unless you can set up in one place with some sort of front rest. For target shooting, these heavy rifles need front support, they are not for off-hand shooting disciplines.
I still enjoy target shooting with my sporters in several calibers, but they max out at 5 shots before a long wait for cooling, and its not a "volume" day unless the air temperature is quite cold. At my local range we have sporter class target competition's of two 5-shot groups (plus foulers/sighters) and 10 shots for score on mini bulls. With my sporter 30-06 and .270, they needs to cool down after the first 5 shots, or they will string the rounds badly. That's alot of powder burning in the thin barrels.
For the combo purpose of use for both target shooting and hunting deer, the 6.5 CM as already mentioned is a good choice, in as heavy a barrel as you can find that you might still carry for a short distance while hunting. The identical ballistic equivalent is .260 Rem (uses same 6.5mm bullets, and a tad more powder capacity). I bought a .260 Rem in the Tikka Stainless Varmint, and have used that for target shooting for several years, and been vary happy with it. Recoil on the bench and with bipod prone is not a problem. I have never used it for hunting, but its do-able. The Tikka Varmint is not the heaviest varmint barrel out there, but its way more enjoyable to target shoot with and can take the heat.
Another good deer hunting option for target shooting is .243 Win with a heavy varmint barrel. But for long range I would choose the 6.5 (.264) calibers for the heavier bullet options for wind performance and energy.
EDIT: I see you do not hand load (yet). That means with factory ammo costs, you likely won't shoot hand loading volume per session (e.g. I shoot 30 to 50 hand loads per range session with my target rifles, which I could not afford with factory ammo). A good way to facilitate barrel cooling with the sporters is to bring more than one rifle. Rotate them in your shooting session to allow each one to cool for a spell. If the Range has a rifle stand for 3 or so rifles beside each bench, this system can work well (use your chamber flags and Range safety protocols). If there is no rifle stand by the bench, it can get awkward if you have to get up and walk to and from the rifle stand area swapping rifles several times per session.