for overheads a large or small diapraghm will work great it depends what your after.
What would be more useful for other tasks /overdubs?piano, gtr amp also can be good with either.
an audix i5 is an inexpensive mic that some really like on snare.
As for micing the bottom it might not be "all that".
Sometimes micing the shell gets more "musical" use for the total sound.
Also a room mic can really be good to blend in with the kit sound , regardless of the
rooms sound this can be useful and doesn't hurt to have to play with later.
also if you later delay this room mic a bit it makes the kit sound bigger and can
extend the tone of the hits:
http://www.electrical.com/phpBB2/viewtopic.php?p=879
Are you tuning the heads of the drums? this gives you resonances that can really
glue the drums into the song or snap them at the song whatever.....
the songs ,