Hmmm. Routers are cruel mistresses. Please be careful with that thang. Make sure you un-plug it before you change bits, etc.
If you are doing just a couple of bodies, then a 1/4" non-plunge will do just fine. You don't need a plunge router when routing the roundovers on the edge. For the interior pickup routes, just drill a hole inside the area where you want to route and start with the bit in the hole - just make sure that the router bit is NOT touching any part of the work before you turn it on. Otherwise the sucker will jump out of the work at you. Just what you need - a sharp out of control blade spinning at 10,000RPM jumping around the bench (don't ask me how I know).
For roundovers, one thing that I would consider if it's in your budget, is a router table. Those work out quite well when doing roundovers and following a template outline.
One last thing: for the outline, saw the work to approximately the outline you want first. Then routing the outline to the template will go MUCH smoother.