Building a motion/activity tracker with AVR Atmega or ARM?
My suggestion would be to start by designing an integrated version of your current solution, by designing your own PCB. Once you have that working, you can decide if there's benefit to you in switching architectures to another type of processor.

ARM processors are significantly more capable than AVRs, being 32bit instead of 8bit, typically having more RAM and flash, and operating at higher frequencies. All of this is more or less irrelevant, however, if you have a working solution on your current architecture; these are reasons to switch only if you need the additional capabilities.

What software and tools you need for an ARM based processor depends on which one you select. ARM is an architecture, but different implementations require different toolchains and hardware tools. For instance, if you use a PSoC based processor, you'll need a Miniprog3 (a type of JTAG programmer) and Cypress's PSoC Creator software. If you go this route, you should find a class of processors that suits, and buy a dev board to start experimenting with.

And yes, it's entirely practical for you to take the next step of making your own PCB.