Hunting around a good aeronautical library Rusty, you should find a lot of information. If you are anywhere near London, ring the RAeS and see if they'll let you spend a few hours in their library if you've nothing more convenient. Apart from normal aircraft design books (and check out Darrol Stinton's "Design of the Aeroplane", and Kermode's "Flight without Formulae" particularly) and aerodynamics books, look up some books on Tornado and MiG23.
If you want a Janet and John introduction...
Swing wings were originally a Barnes Wallis idea, who spent a lot of time experimenting with them on models but never built a full scale swing-wing aircraft. The advantage of them is at high speeds they allow a structurally and aerodynamically efficient high speed shape whilst at low speed they can give good low speed handling and lift. Ideal for an aircraft like the Tornado GR1 which wants to be able to muck about just below M=1 down valleys, whilst still operate from finite length runways.
The biggest headaches are mechanical - the hingepoint is a fragile element, the stores have to be kept in-line with the fuselage, the actuators are very heavy and a single actuator failure can mess up the whole system. Landing a Tornado with the wings stuck swept is difficult and can in some conditions mandate ejection.
Overall, I'd suggest that the aerodynamics of a variable sweep wing are reasonably straightforward, and the engineering extremely complex. If this is what you want, I'd suggest it is an ideal subject for an A-level Physics project.
However, if you feel that you could do with more aerodynamics and more engineering, I'd suggest looking either at Delta wings, or basic aircraft stability - both of which will give you ample opportunities to do mark-grabbing experiments, whilst simulating transonic flow in a school physics lab might be fiddly. Deltas are also where it's at at the moment, I don't think anybody looks likely to develop another swing-wing for a while, but Deltas are all the rage.
G