I'd suggest starting with a store-bought router table. You can find them for anywhere between $50 and $100. Coupled with a low-mid end router, you're looking at a $120-$200 initial investment.
Or you could start off with a very decent
Bosch router and add on Ryobi's more advanced router table ($99) or any other table in that price range. That would be a $320 or so investment total, not including bits.
Really low end starter set: $100-$120.
Low to mid end starter set: $120-$200.
High end router combo with a mid-range router table: $280-$320.
For bits, don't forget that 1/2" shank vibrate less and are recommended over 1/4" shanked bits. Make sure the router you choose has a collet that accepts 1/2" bits.
Amazon.com has great prices on Bosch and Freud bits. I'd say buy one or two bits to start off with, and then keep an eye out for discounts on Freud bits and bit sets.
If you want to build your own router table, that's fine, but there are a few things that can cause the cost to add up quick. You can keep an eye on Rockler, Woodcraft, and MLCS Woodworking for sales on components. MLCS offers free shipping on all of their products, which can be great if all you're looking for is one or two bits here and there.
Okay, so to build your own table, you need:
A power shut-off panel. Your router plugs into this, and then you can easily shut down power immediately by bumping into the switch. This is important in case something goes wrong and you need to cut power ASAP.
Router plate. You can build this yourself out of aluminum, phenolic, or any other suitable low-friction material.
Bit guard. You'll want a guard that goes over the bit in the table so that chips don't fly everywhere.