First time in a studio?
It takes a certain amount of recording experience -- specifically doing one-track-at-a-time -- to become good at working that way. If you want to record like that, plan on spending a lot of time in the studio learning how to do it right.
The ideal situation for a first-time recording project, IMO, is to go into the studio with all your parts and arrangements worked out so the band is tight. Have someone you trust -- someone with a critical ear and good people skills -- work with you during the rehearsal stage to help you work out all the issues (tempo, arrangement, tones, etc.) before you set foot in the studio.
Go into the studio prepared to play your material live without expecting the engineer to correct your shortcomings. A good "live" studio recording can be way more compelling than a recording assembled track-by-track by musicians not used to working that way.
When you're ready for the studio, find a place that has a big enough room that you can play together "live" as a band with enough isolation so you can adjust how and where the different instruments sit in the mix.
"Enough" isolation means that you don't get so much bleed from other instruments that you have to worry much about interference between recorded tracks during mixdown. A decent room and some baffling around the instruments can go a long way toward getting enough isolation while still letting you all play at the same time in the same room and have enough eye contact that you can respond to each other while playing. Don't expect to do this in a budget studio, though. Most low-end studios skimp on the room because real-estate (i.e. square footage) and proper acoustic treatment is way more expensive than flashy gear.
If you're gonna go track-at-a-time, at least try to learn what you're getting into ahead of time. Be aware that most of what you'll be doing in the studio is for the convenience of the recording engineer and not the band. Also realize that your band's sound is in the hands of the recordist and mixer; you're not going to be sure what you have until the very end of the process.
Also, if you're going to record track-at-a-time, rehearse with a click track before you go into the studio; it's a must to be able to play to a click if you expect to get out of the studio in a reasonable amount of time. Without a click, the recordist is likely to spend an inordinate amount of time shifting beats that don't quite line up. The results can be very good, but you're going to pay for that kind of correction.