the PICaxe is nothing but a regular PIC that has been pre-programmed with their special firmware. If you want to use it as a normal PIC, you just need a normal programmer, which can be built or purchased cheaply.
There are a handful of BASIC compilers for the PIC, I can't suggest any particular one because I don't program in BASIC, I use C instead. If you choose to go the assembly route, then you can use MPLAB, which is made by the manufacturer, a complete development environment.
No matter what, you'll need to re-write stuff... but if you take the time to learn to do it in assembly, it will benefit you a lot more than using the PICaxe software, because assembly can be used on ALL the PICs available.