1st things 1st, you're really trying to do too much with too little.

The Mossberg 702 is a 22LR and not suitable for hunting either deer or turkeys.
Deer and turkey are best hunted with a centerfire rifle and shotgun respectively.

Your budget is way too small to purchase a semi-auto anything that is adequate for deer and turkey.

The 1st shot is the one that counts, the more shots you take the less likely you are to tag anything. IMO the best you can do is purchase either a NEF new singleshot 12ga shotgun or look for a used pump shotgun in good condition, use #4's for turkey and slugs for deer. PRACTICE, PRACTICE, PRACTICE and PRACTICE some more.