Fresh heads and sticks is the best advice I can give.
Only record with a click if you're use to it. I can play with or without one. A lot of rock before the mid/late 80s was recorded without a click. Ever wonder why Steve Smith left Journey the first time? Jeff Porcaro has an MI video where he talks about not recording to a click to get more feel from the song because the rhythm section can push/pull accordingly.
Any studio engineer worth their salt will call you before the session and have a chat with you about what gear they have and what gear you have. Trust me if you show up to a studio with a well tuned kit with fresh heads you'll be the engineers best mate.
Take a few snares with you as well (If you have them). Biggest killer of a good drum sound is the room.
1)Practice your parts to a Metronome, record yourself if possible before hand, that way you are sure 100% that what you are trying to do, actually fits exactly on the time ( you'd be surprised at how much fills you may have for your songs, that don't fit exactly on time, but you won't be aware of it until you record. Make sure your parts don't just "feel right", make sure they groove, that they are in the pocket.
2)Start practicing, a lot, everyday... like a lot. Studio time can be stressfull, and there are deadlines, my first studio gig I had to record for 13 hours in one day at the end of the last day, and I couldn't walk the next.
If possible, by the time you go in studio, your body should be accustomed to at least 4 hour long practice sessions.
3)Work on your chops, practice singles, doubles, paraddidles, double parradiddles, flams, quintuplets etc, to a metronome. I strongly suggest Charlie Wilcoxin's "Modern Swing Solo's for the advanced drummer" book, all the rudiments are there, and there are a lot of snare drum pieces that go from beginner to post university graduate skill level. This book, has literally transformed my hand technique, and will make you more confident on your kit ( This may be more of a long term goal than the before studio goal )
One month is not a lot of time to prepare but, if you do this everyday, you should see a substantial increase in your comfort and confidence on your kit.