In my opinion, you really want BOTH an inertia puller and a collet puller. But if you do not have a bunch of rounds to pull right now, just buy the inertia puller first so you will have it when needed. It will work on just about anything.
A collet puller is SO much nicer to have if you are doing more than just one, but there is a little more to know about them. Obviously, a collet puller must have bullet surface to grip, so it absolutely cannot be used on flush mounted wad cutters. But they DO work fine on most other lead bullets. The key is that you will need multiple sizes of collets so that you can find the correct one to use with a specific bullet design. For example, a .38 cal collet will not work with a .38 Spl SWC or TC shaped bullet (of any construction), because the available gripping surface of the bullet is smaller than .38 (actually .35), but a .30, .32 or .338 collet will probably work just fine. Note that the collets have a very small amount of compression available, so you cannot try to just crank one down further to catch a smaller bullet or you will damage it. For bullets with a sloping shape like SWC or TC, the best collet is the largest one that will grip it furthest down to get a larger surface. If you start having problems with the collet quickly releasing a pulled bullet, take it out and use a tiny screwdriver to relieve the pressure on the squeezed collets, then switch to a smaller collet for the job!
For rifle calibers, just having the right caliber collet is probably all you will need, since most of those bullets have ample amounts of surface exposed above the case, but for handgun calibers, you should automatically purchase one or two sizes smaller collets than your target caliber.