Like Nickelthrower said, there isn't really one "best brand" - a lot of it comes down to personal preference. Also, I don't think any particular brand is better than another when it comes to studio recording; the big thing would be your amps and recording equipment/software =)
Here are some really good brands:
Fender: Tried and true; their Jazz basses are one of the most versatile instruments out there, and also one of the most widely used. Their Precision basses are the archetypal instrument of choice for most Punk players. Their 5 strings usually leave something to be desired though.
Ibanez: Another great company; one of the best manufacturers of mid-range basses. Used by plenty of metal bands, but very versatile. Known for superb playability and good prices.
Warwick: Makes VERY high quality instruments, but at a VERY high price - also used by many metal bands, thanks to their trademark "growl".
Schecter: The other kings of the mid-range bass guitar, along with Ibanez. They make some really nice, beautiful basses.
MusicMan: Known mainly for their Stingray, but also for their Bongo and Sterling designs; very nice basses, but also come with pretty hefty price-tags. Very versatile instruments.
There are other companies that make some excellent products like Peavey, Rickenbacker, Spector, Traben...but I don't know as much about them; I'm sure others can vouch for them though. Again, a lot of what some consider the "best" is personal preference. Make sure you play the bass before you buy it, and try out a number of different ones before making your decision (unless it's a "love at first sight" kind of deal =P ).
Hope that helped you a bit.
Cheers!