What's the best food for an audacious jumping spider?

I have a large terrarium where I grow various types of moss. I keep springtails in there to handle any mold that pops up, but some creature (fungus gnat larvae?) was killing off the springtails. So I captured a jumping spider, thinking it would gobble up the fruit flies/larvae. The fungus gnats have disappeared, so it seems like the spider might have done the job, but now I'm worried about it getting hungry.

I gave it a mayfly a couple days ago, and that evening it was sitting in the corner of the terrarium like a toddler with a juice box, so it obviously likes those. Are there any specific things that are good to feed it, or can I give it anything that I catch that isn't predatory? For example, would a "regular" sized moth be dangerous? It'd be like 2-3x the size of the spider.