I'd normally suggest a starter kit but you seem to have all the bits to go with it.
Get an arduino duemilanove from a reputable supplier (ie, not ebay). Tell us what country you're in and we'll suggest somewhere, or you can have a look around this site - I believe there's list somewhere.
You could consider getting two clone boards, it'll work out a little more expensive than one genuine arduino (but not much) and that'll mean you can have one board for running a project and one board for developing on. Somewhere like earthshineelectronics or oomlout are both great if you're in the UK, they sell genuine and clone boards. I believe ebay has a lot of fakes (clones that pretend to be genuine arduinos).
You'll need a USB cable but it's a USB printer type cable - normal USB at one end and fat and square at the other (USB type B I think). You'll need to download the software from this site, and I suggest you get a guide book. There's one available on oomlout.co.uk (decent british vendor) here: link that takes you through the basics, and is handy as a referrence til you get going.
As for wifi, it depends what you want to do really. Have a good google for similar projects, find out what hardware they use and if they've shared their code. Adapting other people's code for your own projects is a great way to learn