The ring won't move, really. The bricks would be more for aesthetics than anything. I wouldn't use mortar. It will be outside and constantly subject to warming and cooling cycles...not to mention water. Instead go with a dry stack brick (or, what I did, retaining wall blocks...they're a bit more substantial and stay in place).

As for ash removal, there's no real need to do that. But when you do need to do that, all you need is a shovel. What the ring is made of is really of no consequence in that regard.

I would spend the time to put in a proper crushed gravel base for the block work, though. A few inches of crushed rock tamped down well will give you a nice foundation for the block work.

FYI, Lowes/Home Depot usually sell a nice fire-ring kit. It will include the ring and blocks to surround it.