I guess it depends on how far you picture yourself going and what sort of budget you have.
Personally, I think the AXE090 is the best way to go if you want to play with more than one breed of PICAXE and don't mind invetsing a few bucks.
I started with an AXE001 and an AXE003 before getting the AXE090.
The AXE003 would be the cheapest introduction but does limit you to only the 8-pin variety.
I still buy the odd AXE021 (just the 08 board) for 'quickies' because even at minimum wage you would have to knock up a circuit in under 12 minutes to break even!
The AXE090 has a built in 7805 regulator and DC power socket which can save a lot of tears for the inexperienced. You KNOW the download socket has been wired correctly, and it has a pull-up plus push-button on the reset line. A feature not many would bother with on a home-build but is very useful for those "won't download" moments caused by long pauses in the program.
I'd say, "Go For It". Also get a couple of 08Ms and an 18X to start with.
Once you've had a play with those, treat yourself to a 28X1.
Not sure what (or if) type of download cable comes with the AXE090 these days but you may need the USB version if your computer does not have a serial socket such as is the case with many new laptops.
Above all, have fun. PICAXE is a great intro into micros and IMHO cannot be beat by any of the competition for simplicity, support and money.