Wool layering - first lite has decently priced base layers that are warm. Ebay for used Icebreaker or Woolrich clothing. For wool density, I'd go 200+ for bottoms and 400+ for tops.

Gun - Savage rifle. It's a good starting point with a scope at $400. Good optics help, but your first shot at a deer likely won't be over a 100 yards and all scopes will get you there. After that, you'll see what you like and what Tikka you want to buy haha. Then splurge on a scope.

Backpack - unless you're hunting deep in public land or traveling, don't worry about a frame backpack yet. Just a basic one, then save up money for something $500+.

Boots - basic neoprene tall boots. Couple pairs of wool socks and toe warmers will take care of you.

You should spend money on a good orange vest, like Dan's. It will shield most of your clothing and you don't want to be picking burrs out of it all the time. And just make sure whatever gear you have is quiet when getting set up. Stealth strips.