a fiddleback bite can be horrid. necrosis ain't no joke.
the thing about spider bites is that they aren't a big deal provided you have quick and easy access to the antivenin.
but without it, well....you might be toast. or really fucking sick for a week.
I don't think there's antivenin for recluse. Very rare that you get bad necrosis, which would involve you ignoring it and not going to the doctor for weeks. Most of the bad ones are likely more from infection than the bite itself. Of course its very rare to even get bitten by them, and even more rare that anything beyond maybe a small lesion comes of it.
Most spider bites in general aren't a big deal even without antivenin, just keep an eye on it. If you know its from a particularly poisonous one then you should probably go to the hospital (if you start getting chills/sweats, nausea blurred vision, then definitely go). Widows aren't even all that bad (but I'd recommend going to a hospital fairly quickly). The Sydney Funnel Web and Brazilian Wandering spider are more serious but again, their danger is exaggerated (but definitely still go to get emergency assistance right away).
Oh, and F*ck you, I'm a Brazilian Wandering spider?
Bonus. On top of being very painful (and possibly killing you), the Brazilian Wandering spider bite can also give you a very painful erection.
As for your spider, OP, I'd guess its a garden/orb-weaver spider. Nothing to worry about.