Hi sputz, welcome to the world of PICAXE.
I'll second Rick's comment about getting one or two 08M's ( or 14M, 20M ). They are very cheap and best to blow one of those up if anything does go wrong when you are first starting out - although odds are that you won't. There's a very cheap project board ( not the project kit ) which can be used with the 08M which has download connectors on. The 08M's etc will likely also be useful in the future in other projects and possibly even in conjunction with the 28.
An idea of your hardware, software and electronics skills and previous experience would help suggest what would suit you best, and any indication of what you are thinking of doing with the PICAXE. If you don't have them, a few LED's and a Piezo sounder will help you experience the PICAXE in real action. You'll want some resistors as well.
A Red, Orange and Green LED will let you build a 'traffic light', add the piezo and a button and you've got the basics for a pedestrian crossing.
I'd personally recommend getting a Thermister ( and DS18B20 if you can extend to it ) as it's fun to watch something change depending on temperature and the IR LED and Receiver is great for infra-red, wireless communication projects.
Plenty of other fun things to be done with a minimum of outlay which will get you hooked ( and illicit shrugs from people who don't have quite the same appreciation for your new found skills ! ). I'm sure we could fill your shopping basket up for you and empty your wallet in the process.