I've been searching for a small robot design that can do that for a few years now, and so far, I have been unable to come up with anything that is actually manufacturable by me (except for one with giant wheels):
-You got tracks and wheels which make the best use of motors, but the size of the obstacle you can climb is dependent on the size of your robot in this case- moreso for wheels than tracks
-Tracks are expensive, but legs are even more expensive and definately do not make the best use of current motors or actuators.
Of the robots that can climb stairs and also effectively move around, they are basically:
-Mars ROver-type robots where the wheels are at the end of legs:
**broken link removed**
-And tracked/tank robot that is large enough
-a monster truck type robot with HUGE wheels
If your sole ability is to climb stairs, I suggest you sacrifice everything else to achieve that goal. You are not going to get a vehicle that can climb stairs and navigate regular terrain for cheap. It's probably going to look very unlike a normal robot (like car, truck, or regular two wheeled robots) since you are sacrificing all other locomotive capabilities in order to make a cheap, small stair climber.
THis is the only one I know of:
**broken link removed**
...assuming legs (in the regular sense) are completely beyond your means, which they probably are. There are research robots out there with legs (based on Geckos) that can climb walls, and trees, as well as snakes that could probably also climb stairs. But they are very complex and very expensive.
If you must stay on the size of the matchbox to climb regular humans-scale stairs, I don't know what I would do. THe only reason insects can get over MASSIVE obstacles relative to their size is sticky feet and wings (and some can also jump really realy far). Since sticky feet and wings are probably beyond your means (or even the means of NASA engineers), then maybe a jumping on is your best bet?
Case Biorobotics Lab
Or you can have a grappling hook and a winch or something maybe? Except you'd need a way to fire it or swing it. Maybe you should just build a small foam ultralight plane and have it fly up the stairs.