Back to the question...
The least expensive starter pack is an 08M with download cable and simple circuit board I think. These days the PICAXE 20X2 is one of the best values of function and program capacity and speed for price... The 08M can do a whole lot of things in a very small amount of program and will teach economy of programming - the 20X2 comparatively has huge programing memory as well as more I/O pins and ADC... Download the manuals 1, 2, 3 and read up on the programing commands and so forth and also look at completed projects in this forum and you'll get an idea of what you may want to attempt.
Also search for your 'real' topic -'what should I start with' as there have been previous discussions and opinions...
I'd start simple with the 08M which I still like... and then go big if you feel the need and learned ability... [I started with Sinclair 1000 & VIC 20 computers...
] The PICAXE BASIC language is pretty restricted compared to full blown BASIC - and it does the job... just not like you may be used to with QBASIC etc... so in learning there will be a lot of syntax errors and checking the manuals [and forum]. PICAXE is a great product at a great price.
Note that you can use the editor [free download] to start writing code and use it to check syntax and do trial simulations... and you can select which chip you are working with in the editor options... And you'll need to hone your skills in planning a program and eventually building some hardware - lots of fun! [and frustrations...]. good luck!