Here are a few example sounds and set ups from my studio

 
Going for a big, fat sound on the large '68 Rogers and trusty Black Beauty snare. Wide open toms for a bit more rumble and a healthy amount of room mic which...
Channelling my teenage self for a 2000's pop-punk type sound, with a Ludwig 400 snare cranked high and Yamaha RC toms. Bringing the overheads down a little t...
Ditching the room mic and lowering the overheads for a more focused sound with dampened drums for this well known half-time shuffle vibe. Yamaha 9000 recordi...
Getting a bit Al Jackson Jr. with this one going for a Stax type sound using just two mics - mono overhead and kick (the side mic you can see didn't make the...

This is an entirely close-mic'd approach to get a focused 'produced' pop-disco type sound. The mono overhead is perhaps an exception, though there is very little in the mix - just enough to lift and gel the kit sound a bit.

I stacked two 10" splash cymbals to get that Roland-808 clap sound which turned out really effective with a little spring reverb!