Ok, to do all the different jobs you've listed, you'll need a lot of planes.
Truing/joining laminates and surfaces:Get a jack plane, you won't need bigger than that (#7 or jointer planes are unnecessary). a Veritas Low Angle Jack plane would be a good start here. Maybe a smoothing plane (#4) to finish up.
Contouring a body: You can get carving planes by brands like Ibex, which are good for this, but power tools or spokeshaves would be a better bet for carving a top.
Thicknessing the neck: More easily done on a bandsaw (cutting the neck profile from the side), or with a router jig.
Radiusing the neck: If you're talking about radiusing the fretboard, then don't use a plane for this, get a Radius sanding block and do it that way. If you're talking about shaping the back of the neck, then Use a spokeshave, or rasps and sanding, more effective than using a plane.
In all honesty you'd be better off getting a router and making some jigs. You could do all the above with a router and a combination of bits and a couple of jigs. You'll spend more on the handplanes, plus there's a steeper learning curve.