Most finishes are touch dry in 12 hours or less. But, if you have the time, you should give them 48 hours to cure properly. Some of the finishes used by lure builders take a week or more to reach full cure.
As stated above, no special tools are really necessary, but a good mini drill would make life a LOT easier.
I've been building for about 18 months, in an apartment, so a nice set of tools is out of the question. My only power tool is a dremel. At the start, I choked at the price and went for the cheapest one on the shelf. Three days later, I returned the burned out shell and bought the middle price option. A week later, the switch mechanism broke, I returned it and bought the dremel!
But you can get by with a normal electric drill that you already probably have, or even a manual hand drill, although this may involve some extra filling operations. Quality, SHARP drills are important. Money can be saved by sharpening your own. Lots of drill sharpening jigs on the market. Once you have sharpened 3 - 4 drills, the jig will have paid for itself.
Hope I haven't damaged your wallet, but don't forget, this is luxury rather than essential. It'll soon be christmas!