Points already been made, but the overheads should give you a representation of the kit as a whole. If that sounds OK, then you can use spot mics on toms, kick etc to enhance those specific areas, but with good mic placement it shouldn't be too necessary. Have you got an LDC you could use as a room mic? That can help give some more colour.
Also, once you've got the track recorded you could try duplicating the overheads twice and EQ one to bring out the cymbals and the other to beef up the toms. Original track can give the full picture. Run it all to a drum buss, duplicate that and parallel compress the duplicate ...sweet. Well, worked for me anyway!