Here's a very good, versatile, set of drum mics that don't cost much, but punch well above their price point ...
Superlux DRK K5C2 ...
We've been using Superlux mics for years, for 'live' or recording, and they do a very good job indeed. OK, there's more in the case than you've asked for, but at that price for them all, they'll be hard to beat compared to three dedicated mics from elsewhere. I'd stress that these are 'inexpensive', not 'cheap'.
For recording drums, I'd recommend using three, basically. One for the bass drum, another for the snare, the third, an overhead. Personally I like to mix the hi-hat into my tracks, so, as an option, I'd mic that as well. Without that, though, the three tracks will do very nicely. Positioning (and room acoustics...) are more important than much else, as even modest mics these days are darned good.
Three for the drums frees up an Xlr for the bass cab mic, which could be handy. There are plenty of videos on how to get good results from a three-mic drum kit; might be worth a look around..? I've a few books on the subject too; ask away if more info is needed.
Make sure your budget stretches to stands and cables, of course. A clip is in the kit case for the snare (and toms...), but a stubby stand for the bass drum and a boom stand for the o/h will be required.
Hope this helps.