I remember enjoying Soul Blazer immensely back in the day, and would like to find a way to play it now. I'm looking for advice and recommendations on the easiest/best way to do that. My parameters are as follows: I don't have a PC, and don't want to spend an enormous amount of money.

Suggestions?

Assuming you own the cartridge and have some way of turning that into a rom:

Raspberry pis are dirt cheap and have no problems with playable SNES games (might not be as accurate as it could be, but it works). Couple that with a cheap bluetooth controller and you are probably looking at <100 bucks to get everything going. Probably less than 60 (30-40 for the pi, depending on the model and any extras. 20-30 for the controller, and then <10 for an sd card).

I looked at ebay, found some cartridges around $20. As long as you're not looking for the box, manual, and new condition then prices weren't too crazy.

Retron sells a HD SNES console for $65.

I can't speak if it's a great experience but generally hear good things about retron products.

For a new HD SNES console that's as close to authentic experience is Analogue's Super NT console at $185.