What considerations should I make for a fire ring?
The long and the short:


Lava rock vs. gravel isn't important except aesthetically.
Use mortar not concrete for binding (in general). All mortar is heat resistant, but you can look for mortar which includes fire clay or get information about mixing your own here (experience suggests that this step is strictly optional, but I will be doing that anyway).
It seems that there are two types of ground level fire pits – ones which rely on temporary insert which is somehow staked down, and ones which are actually built into the ground.