Choice wise I would look at the first 4 on your list with a single rim-fire to start with. There is very little difference between the .303 and 7,92x57 and the 7,62x51/.308 should be listed on your application as just that, so:
.22LR Rifle
.38/.357 Rifle
.303 Rifle
.44 BPR
Ammunition seems fine to me :)
If you have the opportunity to shoot at longer distances and fancy a scoped centre fire the 7,62x51/.308 is the way top go to begin with.
Membership of the NRA does give some personal insurance however if you are not going to venture that far south consider BASC or the NGO or similar as they also have some good deals.
Finally, welcome to the forum
