Personally I try to maximise the snare in the overheads so I need less of the close mics.. current favorites are my Beyer M160 & M130 ribbons as a mid side pair, with the M160 aimed somewhere between the snare and the rack toms.

Generally overheads are supposed to pick up as much of the kit as possible not just cymbals. I generally get the overheads and kick mic sounding good together then introduce the remaining close mic'd sources, but I really want my core sounds coming from my overheads. Try appoaching it that way.

Ok

Quality small diaphragm condensers. I have excellent condition Neumann KM84's and KM86's that do a great job. I also reach for Schoeps CMC6 MK4 (their modular cardiod microphone) which are easily just as good as above, actually a bit flatter than the 86's and a bit bigger and more accurate than the 84. I too try to maximize snare and toms, I don't have to use room mics and the snare and toms always sound fat and punchy when combined with some close mics.

i usually find that the snare amount that goes into the overheads is just enough to give the snare a credible brightness that it wouldn't have if i would only use the snare close mic. if you want to minimize the snare in the overheads you could put them like 60 to 80 cm's apart and tilt them slightly outwards, away from the snare. this should create some kind of "hole" in the middle, where the snare is. if you put the mics closer together you'd fill up that hole again, of course. but i never found that to be necessary, i think the set will sound more artificial if you use only the spot mics...

if you're going for the modern sound of today (i mean the punk/pop/core/stuff), you shouldnt worry too much about the overheads. its more close mics and rooms that do the trick there.
spotmic some cymbals if you need 'm but most of the time these guys like to smash the crap out of the cymbals so you already have enough on everything else.
its more in the postproduction phase that you'll get a fatter tone nowadays, like snare-doubling or sample-replacing kicks/toms/even snare..

if you're going for the milder/if-you-want-more-realistic sound, i'd suggest you start with two overheads and a kick mic.
just keep fiddling around.
i like having them low (about shoulderheight, and behind the drummer) pointing towards the middle of the tomtoms.
most of the time you'll need an extra snaremic too. add that in.
then maybe add a little floortom.
i usually have enough signal with only 2 oh's and a kick and snare. its great to fiddle around with!

good luck
recording drums is the shit, so have fun

Keep the Snare in the Overheads

I much prefer having the majority of the snare in the overheads, only using a little bit of the close mic for definition, especially during intricate rolls.