Like mystic96 says, if you are planning T-molding a router will be mandatory. Personally, I subscribe to the "buy things once" school of thought, so I wouldn't cheap out. You don't necessarily need to spend $300, but I'd probably budget around $150 or so.
Routers in arcade building are generally ideal for:
1) Cutting both sides of the cabinet to exactly the same size; a flush trim bit works for this.
2) Cutting a plexiglass top to match the top of the control panel; again, flush trim bit.
3) Making perfectly smooth curved cuts (using a jig made out of a length of wood).
4) Slot cutting, for T-molding.
5) Routing out areas for flush-mounting joysticks or other hardware.
6) Trimming laminate, if you decide to go that route instead of paint.
So yeah, a router is recommended. FWIW, you *can* build without one. I made my first control panel without a router (actually I tried to use one for routing a T-molding slot, but effed up and made the slot too big). I even cut a cover out of plexiglass without using a router, but admittedly it didn't fit the best. But once I got a router, I can safely say I never looked back.
And yes, when using holesaws you have to remove whatever gets stuck in the saw when drilling. A bit of a PITA, but the nature of using hole saws.