Do your homework and write down what the studio has to offer - microphones, preamps, EQs and compressors - and then do some research on the internet, there are many forums with a lot of info, like www.gearslutz.com (where recording/mixing/mastering legends like George Massenburg and Bob Katz are moderators).
For a solo act, a good quality microphone might be sufficient by itself. But for a band, you want to have access to different microphone flavours, because if you overdub everything, even with a premium microphone, the final product will sound flat. A good quality studio has to have a good collection of microphones, because each style of music and each instrument requires a certain sound and, there is no one type of microphone that fits them all.
If you want to record a concert piano, a matched pair of omni Earthworks or DPA and a large premium condenser are the way to go, especially for classical music and jazz. Of course, two Rodes or AT will do the job, but YOU WILL HEAR THE DIFFERENCE! For reeds nothing beats a good ribbon mic. And staples like Royer, Coles, AKG 414’s and 112D, Shure SM7, SM 57, SM 58, Electro-Voice RE-20 and MD 421 Sennheiser are a good bet for drums, percussion, bass and guitars. While the most important thing for getting a top quality product is the artist performance, the studio has to be able to provide the right tools to capture that sound.
Regarding the preamps: make sure the studio has premium preamps, which are suitable for the style of music you are playing. If you’re a classical musician, or for acoustic instruments, a transparent preamp like Millenia or Earthworks is desirable; for rock, jazz and R&B preamps like Neve, Focusrite Red, Martech, API, Pendulum Audio, Great River, SSL, Fearn, Vintech, Avalon are great options. There’s a reason the Millennia preamp is used almost exclusively all over the world for classical/chamber/choir music, where "clean" and "headroom" are the name of the game.
Of course, great preamps are not cheap. They do cost thousands of dollars! In your studio search you will be told how great Presonus, ART, Mackie and Behringer preamps are. Here is the news: they’re not! They're not bad, they’ll get the job done, but you can’t really compare a 1500 dollar one channel preamp with an 800 dollar eight channel preamp or mixer! Look for a studio that has a couple of great different preamps, so you can take advantage and get the best in different recording situations! API, Focusrite Red, Neve or SSL are great for drums; on the other hand, when it comes to record or warm up a synth, a tube preamp like Pendulum, Thermionic or Fearn is a great way to go.
You can skip this paragraph, it’s going to be little technical, but it gives you a better understanding of why a microphone preamp does a good job. Most everyone knows that we have to avoid clipping during recording; what is not widely known is that, long before clipping, many preamps exhibit an extreme distortion increase, as they change from Class A to Class AB operation. Therefore, it is very important to have at least 6 dB between the peak level of the music and the clipping point to avoid a harsh sound. The difference between the average level of the sound and the clipping point is known as headroom. The bigger the headroom, the better the sound! The high-end preamps have clipping points as high as 37 dBu (+55 Volts), while the semi-pro and consumer equipment have 20 to 24. In plain English, in order to get a good sound, the preamps have to have very high output devices and high-voltage power supply, which is very expensive; you won’t get that with 100 dollars per channel preamp. These cheap preamps are good for the hobbyist recording engineer, but they are to be avoided if you are looking for quality! The good preamps or EQ include very high quality circuits and excellent transformers, and when you have to mic many tracks, you’ll understand it!
Pay attention to the vocal chain- make sure there is a great vocal compressor like Tube Tech CL-1B or the LA-2A, eventually a Cranesong Trakker. They do a great job without compromising the voice quality and, when used properly, you can’t tell that the voice was compressed – they’ve got a magic touch. Great vocal preamps are Martech MSS-10 (very deep, great for huge voices, huge headroom, many consider this to be the Ferrari of the mics world), Neve 1073, Pacifica, Telefunken V72, Hardy, API. As far as the vocal microphone, you want to be able to choose from a selection of great microphones to see which one fits your voice best and make sure you are given to try at least one high-end tube large condenser.
Always ask about the quality of the A/D and D/A converters. If the studio uses tape, that's not relevant, but if the sound is recorded into a computer, the converters are the first thing you want to look at! There are audio cards with converters like Motu, Lexicon Omega, Digidesign Mbox-2 or Echo which provide a good sound; but when it comes to a great sound, with extremely reduced artifacts in the process of conversion from analog to digital for recording or digital to analog when listening, look for mastering grade converters- Prism, Mytek, Lynx, Lavry, Apogee. When the track count is high, you’ll hear clearly the difference! The aforementioned mastering grade converters are way more expensive, and, again, there’s a reason why. These converters provide higher integrity to the sound and they employ very sophisticated jitter reduction technology. In plain English, they almost entirely preserve the quality of the sound during the conversion to digital or to analog.