I'm planning on doing a web series later this year and I was thinking about how many viewers would be watching on fairly small monitors attached to their computers.

I'm wondering if I should not try any shallow DOF and avoid busy backgrounds, because most people wouldn't see it anyway. Instead I'd use very contrasting colors (like yellow and blue) as much as I could because on a small screen it would be easier to see what was happening.

I'm a little spoiled because I have a 32 inch HDTV as a computer monitor. So when I watch stuff online, I see it pretty big. If I had to watch it on a 12 inch monitor I'd be straining to catch the details, and I wouldn't enjoy it too much.

Anyone else have those considerations? Or am I over concerned because I'm putting something on the web?

In my opinion, you want to create the best experience for the widest possible audience. In general, this would mean good SD video as opposed to HD.

Shallow depth of field still flies in good SD, very high level of detail and busy backgrounds usually don't. Contrasting colours might not be the best approach, though, because while low spec monitors would benefit, it may look hideous and heavy-handed for those with average-to-better displays. I'd suggest shooting colour normally- the web encoding will compress the material anyway and a low grade display will still show it as best it can.

I would say though, avoid overly dark scenes. LCD displays- particularly on laptops- don't have the range in black areas necessary to see detail. You only have to look at a lot of "film-look" material rendered with post-software (with it's gamma and black stretch tweaked to look like celluloid) to see a murky black mess where there should be gradual detail.

Although you haven't mentioned composition, aim for TV-style framing rather than the cinematic because the scale cinema uses for wide shots really doesn't translate that well to a small youtube window or a 15in monitor. Close-ups are your friend. Try to light and mic and mix as you would for a better transmission medium- it'll raise the production value even on cheap displays and laptop audio.