That Dewalt is probably a nice bit of kit, but quite expensive for a 1/4" router.
In my opinion, you could happily use 2 routers to build solid body bass/guitars. A big 1/2" router is good for routing the final body outline with a template and doing the trussrod channel. A smaller 1/4" router is great for pickup and neck cavities, binding, etc.
You can use a big 1/2" router for the smaller jobs, but they are big, heavy and most people are scared of them. They are a good choice if you are burly, are going to put them in a router table, or have other uses for a router - maybe you want to also build furniture, do DIY, etc.
1/4" routers are much easier to handle for finer tasks and can be pushed to to body outlines and truss rod channels at a pinch. They are perhaps a safer choice for a 'first' router. Bosch 1/4" routers seem to be popular with luthiers, and Stewmac sell one of these. [Edit, I see this was mentioned earlier. In fairness, the Bosch routers are a lot cheaper than the Dewalt recommended, which may explain the popularity].
If you want a big (1/2") no-nonsense router that is 'trade' quality, a relatively cheap option is the Hitachi M12VE/ . I have one of these, and can testify it is a beast. Dust collection is pretty terrible, but not a problem if you put it in a table, which most people do. Above table adjustment requires a router raizer or lift, which isn't ideal.