If you do end up using cup and core ammo the .308 will definitely be hard to beat, some others will have slightly better ballistics but any deer won't care.
However if you end up using monos or bonded projectiles that might not be the case.
I'd talk to a few gun shops and see what ammo you can actually get, try and stockpile 40+ (depending on how much shooting your doing) rounds of a few different loads. Keep the one that shoots best and sell the others. Then go and buy a rifle in whatever caliber it is you've actually got ammo for. Of course you won't actually be able to take the ammo home but most shops will hold stuff for you if you pay now. (it's only getting more expensive)
Within 300m anything from a 243 to a 300 mag is going to be fine, suppressed the recoil will be tolerable as well.
Monos do work better when there going quicker so if you end up with options I'd get the faster one.
Of course if you're shooting targets I'd use a cheaper hopefully more available option than the flash ammo. Also an accurate 22 lets you practice and shoot without worrying about using heaps of rounds.
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