There are definitely a lot of options! It's a little mind-boggling at first. Spend a bit of time on gearslutz.com, watch some microphone shootout videos & familiarise yourself with the specs of different options. Like drums, within a certain price range/quality bracket it becomes a question of sound/taste.
I acquired a "set" piece by piece off eBay/Kijiji (Cdn Craigslist) recently. I was trying to get something usable for home recording on a quite limited budget ( and live when really needed), but also wanted to get something good enough to not replace them too soon down the road. I ended up with:
Shure SM57 (tried & true)
3 x Audix F10 (toms)
1 x Audix F12 (floor)
2 x Shure 849 (OH), older model that can function with batteries for 48V
1 x Sennheiser e602-II (kick)
I'm quite happy so far! Audix drum mics are known for their colour, not their "flatness", something to keep in mind. I tend to hone in on the mids & highs I want and trim off some of the "phat". The Sennheiser E604 tom mics we use in our basement studio are less aggressively coloured, a little more "natural", but with a little less rejection than the Audix's.
The Sennheiser e602-II (kick) also has a "coloured" tone & is within the realm of an Audix D6 (modern low, lots of sub, scooped out mids). Again a kind of semi-"plug & play" mic, which can be practical for clubs that have PAs with limited EQ. It's good for a modern recording, but I have access to a vintage AKG D12E, which is just a pearl of a kick mic! Not exactly affordable though. Folks seem generally divided between the Shure Beta52A (more of a natural mid shape), Audix D6 (the Emad of the mic world), AKG D112 (flat, "boring", but some techs swear by them, Heil Sound PR48 (Big and full sound, little bleed, bit more expensive of the rack). I'm forgetting a few (too early), buy my point is that for BD mics you'll get as many replies as asking which BD head is "best" on MyDrumSet on FB. Watch some shootout videos on Youtube, familiarise yourself with the colour palettes available and choose one you like within your budget.
The Shure 849 (overheads) are the other way around, much less "hyped" in the high end than a lot of mid-priced modern pencil mics. They have a nice enough bottom end to envision using them in a 4 mic setup & like to capture my lower pitched cymbals (the HHX Legacy is way low for a crash). Again there are a zillion options, from Samson to Neumann in price. I lucked into the Shure 849's, but a lot of folks liked models by Rode, MXL & Octavia for affordable OHs when I was doing my research.
The Audix i5 is a popular alternative to the Sm57 for snare miccing & has a bit fatter low end, likes deep, low tuned snares.
Keep in mind that many mics can be used for many things and investing in versatile mics like SM57's & Sennheiser 421's is always a good move. Between the 2 you can theoretically do pretty much anything. I also have an ancient Electro Voice EV 635 dynamic mic that has been used in the past on Elvis's voice and vintage recordings of BD's. It can handle the SPL and has a nice warm "vintagey" low end & I picked it up for peanuts.
Spend some time reading about different mic placements (Gly John's above, the Recorderman variation, XY (Coincident Pair) pattern etc...) and spend some time experimenting. This has been super satisfying for me, though i'm a very patient guy when it comes to "geeking out".
I didn't want to over-simplify, so sorry for the long rant...Hopefully other will chime in, agree, disagree with my opinions and give more perspective.
