The trick is to use sandpaper. It’s a good quality abrasive material and is readily available. You’ll want a selection of different grits – low grits to get started, higher grits when finishing. The reason this is cheaper is that you can get a selection of 5-10 different sandpapers for under $20. Getting even a couple of decent sharpening stones wouldn’t be possible at that price. In the long run, they’ll last longer but this is a budget option we’re talking about.
To get the most out of your router, you are going to want a router table. You may find yourself asking if you really need one - if you do, check this post out. It's one of those purchases that you won't truly understand how valuable it is until you have one. Given the budget of $2,500, I'd suggest looking at the Bosch RA1171 ($150). If you want to see our favorite tables along with write-ups, check them out here.