Well it all depends on the quality of recording you intend to do. I mean, if you have unlimited finances, go Sure mics all the way. Other than the usual top brand names (Roland, Marshall, Rhodes) I don't think it makes much difference, so long as they're not broken. You should be able to get a nice sound out of any specified drum mics.
As for the types of mics you'll need, start with a purpose built bass drum mic for the kick. These mics are made to record only the lowest end of sound and to withstand the shockwave of the kick without changing the sound.
Tom/ snare mics are also purpose built to add a little extra punch to the sound, whereas regular dynamic mics would not.
Hi-hats you can probably get away with a standard, balanced dynamic microphone, or possibly nothing at all depending on how important the sound is and how good the next items are.
Overhead mics for drum kits are usually condensor mics. These mics are capable of making the high-end of your cymbals sound crystal clear, but unless your mixing desk has assingable phantom power, be sure to buy mics that carry their own battery.
Most drum mic kits will have all these mics included, except for the hi-hat. If the company has gone to the trouble of making a pack like this, they'll probably do the job. Thankfully you have a pretty standard setup, so you should have no problem finding a set to suit your kit.
You'll need, One kick mic, four snare/tom mics and two battery powered condensors and maybe a dynamic mic for the hi-hat.
Of course, Look out for packs that include cables and rim mounts, these can be a godsend when you first start putting it together and you're missing one stand or lead.
Anyway, I hope this helped and let us know what you end up with.