First time bow hunting, looking to get my feet wet.

Never shot a bow or really had much interest in it.

I know bows are "sized", I am a big guy, 6'7 360lbs, not sure if anything "off the shelf" can be had.

I was planning on spending around $300ish, is this even a realistic budget?

Help!

Guessing that you're looking at compound bows, $300.00 might not get it done once you add the required accessories.  Bow by itself, maybe.  Find a good bow shop even if you have to travel a bit.  Get your bow set up by a pro.  Skip the "beginner" stuff.  Learning to shoot isn't that hard.

I was planning on hitting some places this week at some point, just looking for some suggestions

https://www.americanhunter.org/articles/2019/2/15/2019s-top-compound-bows/

https://hunthacks.com/choose-compound-bow-buying-guide/

Here's a couple of quick reads that might help.  Lots more data on the web.  I shoot an old Hoyt and a McPherson.  Every one has there favorite.

imo try finding a nice shop close by and see what they have and can set you up with. imo you are better off buying a older used but still good mid range bow from a few years back then a new beginner bow.

just like ar15's bows can be customized and will start costing a lot of money fast if you start buying quality stuff. also arrows can get pretty pricey fast.

an easy thing to do is measure your wind span and divide by 2.5 to get a starting draw length.

would look at getting on archerytalk .com and get 20 posts to look at their classifieds to get some deals on used bows and other equipment.