This is kind of what I was getting at above before I deleted it because I started going off on my own trip. I've been working on drums sounds too as the OP. There are just too many ways they can sound. You just have to experiment with different things until you find the sound you like. Adding the compressor will change everything including the sound of the overheads. But it may fatten up the snare or kick. But you can get a fatter snare by moving the kick mic in more and adding low end too.
You also noted that you should experiment to find a sound you like. Then you may also find that different recordings should have different sounds.
I've generally taken a big picture approach, treating the drum kit as a great big thing I want to record, not several different things.
Typically I use one, two or three mikes. Usually my Shure SM80 omni mikes. Usually one overhead. If I could get away with just one mike, I would, but usually there is no single spot that gives a good, complete sound. I have the kit surrounded by 10 to 12 ASC Studio Traps, which helps a lot. It creates what they call a Quick Sound Field in the space of the kit and especially where the overhead mike is. That means that the mike hears a lot of diffuse, quick reflections (that kind of compress the sound in the air itself and add some body) and then a quick decay so the sound is lively, but dry. It also tames the low end down to about 100 Hz and gets rid of most of the reflected sound from the room. Not much point in trying to record room tone in a room like mine.
The overhead mike gets a lot of the kit, but the kick is just kind of an ethereal low end suggestion and the snare has no rattle sound to speak of. That works OK for a calm, jazz sort of mix, but not so much for something loud and energetic.
So, usually I have another SM80 a few feet out in front of the kick (about a foot off the floor or perhaps higher) that gets a fuller kick sound and I cheat the mike over to the snare side a tad so that I can get some snare rattle. It also adds some strength to the rack toms.
Those two mixed in mono (or maybe tracked separately and panned a little bit) is often just what I need from the drums, though the floor tom might be a tad weak. Since I don't compress the overhead, I usually have to remind myself to play consistent and balance properly between snare, toms and cymbals (i.e., hit the snare and toms hard).
The third mike would typically be over my right shoulder or down a bit closer to the floor tom.
Typically the result (given the limitations of my playing and the sound of my homemade kit) is a big, open and fairly complete sound, though fairly dry. I don't work too hard to try to do complicated stereo stuff, because I usually find that mono or a bit of panning of the two tracks is fine in the context of the mixes I do.
I don't seem to have many phase issues using just two or three mikes. The mikes are sampling such different parts of the sound that it doesn't cause problems. If I'm using that third mike, I usually try to keep it the same distance from the snare head as the overhead mike, though it's usually far enough off to the side of the snare that it really isn't getting much of the body of the snare, just some rattle.
Tracked and mixed to tape it gives a good solid drum track with very little fuss. Maybe a little bit of eq to adjust it to the other tracks, but usually I don't hear much benefit from compression.
Cheers,
Otto