You don't need a plunge router. That's only if you plan to start routing a groove in the middle of a a surface. In all my years of woodworking I've never had a plunge router that I've liked or much used the plunge feature.
You could get just about any router, but as a router is an extremely useful tool and often the difference between an OK project and a good one I'd strongly recommend the PorterCable 1001 3/4 horse router. My dad still has his from about 1954, I've still got mine from 1977. It's a great machine. You adjust the depth by turning the motor in the base-it's like a 3" diameter fine thread bolt. That makes it easy to tweak up and down in 1/256ths of an inch when you are setting up your bead and cove.

Also using it in a router table, you can buy polycarbonate bases that fi this model, or you can make your own out of plexiglas. Rockler.com has bases for this router. No, you don't need to buy a router table.
Also I'd recommend that when you cove and bead your strips, cove last. Nick recommends this in his book. But there's another bonus if you cove last and leave your table set up. You can rout coves in strips you've planed down for fitting. While it's easy to knock the corners off and make a bead with a hand plane, coves are much more difficult. You can carefully hand feed them along the router fence and cut new coves. You'll get better coves quicker.
Wear safety goggles and a good dust mask.
Also be careful with long feeds into any router. Watch that you're not sending long slivers off your bit, These can be forced into the motor-which will cause you to have to get the motor rebuilt.
Tighten but don't over tighten the bits & sprinkle a little grahite on the bit shaft. This will help prevent the nut from seizing tight.
Will

: Also, how many horsepower do I need to get? I can get a 1 hp plunge router
: for $39.99 or a 3 hp for $79.99. I probably wouldn't use it much at all
: except for building this boat, so I'd like to go with the cheaper one if I
: can.

: Thanks.