Nice one, Dave!
I've avoid trying to cut a bottom groove in retrospect. Use drawer slips, like you would in the best work. If you're not familiar with the expression, a drawer slip is a moulding with a groove cut in it to take the bottom. Tradionally it's glued and pinned on the sides and front of the drawer, mitred into the corners, and you slide in the bottom, no glue, and pin to the underside of the back.
If the ASCII art works, this is how it looks in profile.
___ |_ | _| | |__ |
The top internal corner is usually rounded over to avoid snagging clothing in the drawer.
Although it involves slightly more work and the loss of a small amount of internal drawer space, this system is generally accepted as a better system than grooving the sides, since it avoids weakening them, gives more bearing surface for the drawer to run on, hence less wear, and it's easier to repair things when they fall apart/wear out. For a drawer the size you describe, I'd guess the profile would be 1" or so deep and around 1/2" wide, the groove being abou 1/4 - 5/16" deep.
HTH
Frank