I'm a novice with woodworking. Want to build a microwave stand with
cabinets and other shelves that will be about 6' tall. I figure using a
dado blade of some sort would be best for the slots for the shelves. Is
the blades for my table saw the best option for making the straight line?
How hard would it be with a hand held router?

As others have mentioned, the dado set may be faster (once you get it
set up), but a router will be FAR more versatile and a better choice
for your first purchase. It is not difficult at all to make a straight
dado with a router - clamp a straightedge to your workpiece such that
the rotation of the router bit pulls it TOWARDS the straightedge, and
you're all set. If your dados are quite deep, you might take 2 passes
at successively larger depths, but a 3/4" bit with a 1/2" shank should
make a 3/8" deep cut in 1 pass.
I think there a few recent threads here about good beginning routers -
check out just about any woodworking magazine or patwarner.com for a
large-scale comparison. Something in the 2HP range from one of the
real name brands (i.e. PC, Dewalt, Bosch, etc., not Skil or Black &
Decker) will be better quality and last longer.
Good luck,
Andy