What should I place at the bottom of my couch to prevent miscellaneous items from going under it?
I think the most common solution is to just let stuff slip under your couch and move couch every once in a while and pick up the stuff.  

If you want to get fancy you can get some metal "L"s from the big box around you and screw them to the bottom of the couch to create a "crap barrier".  This would take a couple of cuts and 4-5 screws per "L".  $10-15 and 20 minutes.  If you want to get really fancy you go to the nearest fabric store and find a fabric and possibly padding (so padding first then fabric) and then staple these over the L brackets.

In the end though I feel like this advice may give you a false sense of under couch security.  Stuff is still going to find its way under there no matter what you do.