Steve, You will need to purchase a router that accepts guide bushings in it's sub base plate to make your circles using templates, or a circle cutting jig that attaches in place of the routers sub base plate. Before making a recommendation on which router would be a good choice we need to know what else you plan to do in the future.
We are familiar with HDPE and UHMW since many of the jigs we use are made from these materials. Keep in mind you will not get square corners from a rotating round bit, however it is possible to make corners with an 1/8" radius and that may be close enough to square for your needs.
Jigs can be purchased by clicking on the yellow Oak Park banner ad on this web site, at Rockler or Woodcraft stores & websites. You may also have other tool stores in your area which carry woodworking supplies.
My personal choice for most router duties is the Bosch 1617 router combo kit. This includes a fixed and a plunge base, an adapter for using guide bushings and both 1/4" & 1/2" collets to accept your bits. The 1617 is a 2-1/4 HP quality machine. The new Hitachi combo kit, Porter Cable or DeWalt kits are all good choices. Expect to pay around $180-230 for these routers. Don't go crazy buying bit sets, spend your money on decent quality bits for the job you are working on and build your collection that way. Woodcraft often sells their own brand of bits for $5 each; these are decent quality and perform well for me.
"Living in the D" (this means Detroit!)
"It's fine to disagree with other members as long as you respect their opinions"