I am using plywood for the drawer bottom of my little table. While there are cabinet quality plywoods available commercially, I prefer to make my own for a piece this size. Plywood offers better stability than solid wood and is easily made to your own specifications. I chose top and bottom veneers of pear wood and a center cross band of oak. It'll be plenty strong for a small drawer and the pear wood has an elegant, subtle character.
Veneers are cut on the bandsaw, run through the planer to a thickness of 3/32" then glued up as a 3 layer sandwich between a couple of MDF cauls.
Blue painter's tape and waxed paper keep the whole mess under control. A printer's ink roller is used to spread the glue evenly between the plies.
I use every clamp I can get my hands on.
Once the glue has cured I trim to size and hand plane a combined 32nd of an inch off both faces to complete this 1/4" thick plywood drawer bottom.
You might ask "doesn't this take a lot of extra time?" To this I would reply "yes".