The most important thing is to get started, and I think that you have more chance to get started with an Arduino or PICAXE quickly then any other alternative.
I know that once you have your programming environment organized, programming on ARM or TI processors can be as efficient as an Arduino or probably even better. I remember developing a multitasking real time operating system for 8051 type processors, and once the operating system was set up and debugged, the rest of the programming was very easy. But it took a lot of time and effort to reach that point.
I also remember with the 8051 project how long it took from the start of programming to the point the hardware could start to do something useful. It was months, and a beginner wants to see results on the first day.
If you are new to programming, I think you are going to go from idea to something that works far quicker with something like an Arduino then a MSP430 or ARM system.
Sure, you will outgrow the Arduino or PICAXE and that is good. You will probably realize that microcontroller code you develop from scratch can be far more reliable then code that uses libraries from unknown contributors and of unknown quality. That is good too.
If you start with an ARM development system, there is probably a 99% probability that it will sit on a shelf for the next 5 years. Then it will be out of date.
If you start with PICAXE or Arduino, there is a good chance you will be getting results in the first day without having to install development environments that are gigabytes in size, without needing to learn an IDE with thousands of features, without having to make sense of datasheets hundreds of pages long, and without having to make your way through language references thousands of pages long.