"pin drill" of some description and some itsy bitsy teeny weeny yellow polka dot bits.
I've ended up with about 3 different pin drills (a plain metal one, one with a large wooden knob for a handle, and an Archimedes one), and a little battery powered drill thing as for different materials and sizes of bits different ones work best.
A general pin drill (you can get them from about £3-5 up) will do most thing for modelling, but can be quite tiring/hard on the fingers and hand if you're doing a lot of holes or into metal models (I got the Archimedes and battery ones after getting some blisters from pinning a bunch of metal models).
Also look at buying the bits from somewhere like screwfix rather than model stores, IIRC last time I needed some I paid about one or two pounds per pack of ten from a DIY store.