The Basics!

The equipment you need varies with your level of
accomplishment, and your playing venue!

The beginner needs a guitar, or bass that plays well, and,
if it's an electric, an amplifier just big enough for home use.
Five or ten watts should be plenty for guitar, double that for bass!
The guitar doesn't need to be fancy, but should be
designed for the kind of music you wish to play!
Heavy, hard rock requires a humbucking pickup in the bridge position,
and possibly a locking tremolo.  For alternative music, a variety of pickups
would be useful, and the tremolo could be non-locking, or even be omitted entirely!
For country, two or more single coil pickups (or humbuckers that can be switched
down to single coil) will give you the "twang" you'll need, and the
bridge can be fixed, non-locking tremolo, or locking tremolo as you wish!

Bass players should keep in mind that longer strings sound deeper, and since
basses are available in several different scale lengths, you should choose the
longest bass that's comfortable for your hand size!  But if you have very small hands,
don't worry, a shorter bass can sound OK if you know some tricks, more about that later!
The most popular pickup arrangement for basses by far is the so called "PJ" setup.
That is, a split, staggered "Precision Bass" style pickup near the neck, and a
straight "Jazz Bass" style near the bridge.  The variety of sounds available
from a "PJ" setup will handle almost any kind of music!

When you start playing together as a group, those needs escalate,
especially if the group has a drummer!