ez-willis' advice is solid for getting the best pitch from your drums. Timbre (which is a lot of what you are looking for) is also heavily determined by the heads you are using on both sides, among all the other physical characteristics of the drums.
Try to get in a drum shop that tunes their kits well and pay attention to the heads on top and bottom and how they are tuned relative to each other. Get some heads that have the timbre you're going for and tune them over and over again until you find what you want...then see how they sound in your room, under your mics, through your signal chain.
I've been trying a lot of heads from all three big brands recently on a lot of different drums and playing them in a lot of different spaces. I find it amazing how a drum that sounds fantastic in one situation with a certain tuning can be useless in a different room, etc. Now I always have three bass drums, three snares and a selection of toms that I put a kit together for whatever the gig's specifics require.
Oh, and location of the kit within the room has a major factor in the overall sound that reaches an audience or your mics. Get out of the corner or back in, depending on what characteristics you are looking for.
