Hey Drew, welcome!
See, the thing about those etsy and eBay shamisen are that oftentimes the skin is broken, or they’re otherwise just not in good condition. And to fix the skin or any other issues might raise that price point quite a lot.
But it IS totally possible to start around your budget! Or at least will be, once you get to around that 500 if you want higher quality synthetic skin as opposed to natural or plastic.
I don’t know which style you’d like to learn in particular (tsugaru, nagauta, jiuta, Minyo, etc) but any of these can be started on any kind of shamisen, at least.
Personally I recommend the Beginners Shamisen from the store here - it’s between 350 and 550 dollars depending on your choice of skin, and it’s actually a pretty nice instrument despite what is in the grand scheme of shamisen a low price. It sounds great and is a wonderful place to start! If you don’t want to worry about a natural skin (which could tear or be otherwise damaged without proper care) I think the Fibersen is worth it, it sounds great and holds up great against the changing weather.
Other options include, if you can find a reasonably priced one, something like the ST series shamisen which you can find on eBay - the thing with those is that the synthetic skins on those are much lower quality than Fibersen or ripple and sound very flat and clunky, and that’s coming from someone who started on one. But it’s a very serviceable instrument to start on with matching expectations and a hope to one day upgrade.
Eventually you’ll want to upgrade no matter what, but of your options I think the beginners shamisen here is a good way to go. It’ll be more rewarding of it sounds like a real shamisen, which it really is. The other less expensive ones are generally much lower end and aren’t always easy to get full enjoyment out of.
I hope this helps!