Your regular drill bits and such should work when you are starting out. As for wood think about what you want to do. For portraits like people do the easiest is baltic birch. The most common thicknesses are 1/8" and 1/4" so either one will be fine.
For things like puzzle like those animal type puzzles you see just use some basic pine boards.
no sense getting too wrapped up with too much money when first starting out.
You will need some blades, its possible to go through a lot of them at a single sitting so spend a few bucks on getting a lot of them. Flying dutchman, olsen, pegasus are a few that people use. i prefer flying dutchman and many will agree on these. They are sold by size so look up a size chart, easy to find online. An example would be a #7 would be for thicker stock, the numbers will go down the thinner the wood gets so for starting out on a pine board that is 3/4" thick you will be fine with a #5 blade, for thin wood use a smaller number.
Its best to but them online as most stores just dont carry them and it will drive you nuts looking for them. woodenteddybear is pretty much the outlet for flying dutchman blades.
you will see a bunch of types as well. i use fd-sr, flying dutchman, they have reverse teeth so they cut on the up and down strokes so it leaves a smooth finish without a bunch of burrs. also fd-ur will work great.