Frankly, I don't use ratchet / sockets much when working on bikes. The vast majority of fasteners on all but the cheapest kid's bikes are usually Metric Hex Socket screws / bolts. Get a couple nice sets of 'Allen' hex keys. Get one 'L' set and one T-handle, both types have their advantages.

For opening up headsets and wheel hubs, a ratchet and socket are pretty much useless. For hub cones and lock nuts, you will need a set of Cone Wrenches, which are stamped-steel crescent wrenches with very thin (~2mm) jaws, since hub nuts are about 1/3 the thickness of a 'normal' nut. You can buy them in sets or individually, 15mm and 17mm seem to be what every thing in my fleet has.

For older, threaded headsets and BB's a 10-12" Thin-Jaw Adjustable works well. Park Tool makes a specific-size headset wrench, but if you're dealing with older / cheap / kid's bikes, you may run in to non-standard sizes.