so what's the max amp rating the regular moto g can handle?
Using an old wall charger that says it has output of 580ma at 5.2v - means it has 0.58amp charging ''speed''?
0.58A is the maximum amount of current your current adapter can supply, the Moto G 2015 is capable of drawing 1.0A (actually, about 980ma is the highest I have seen according to GSAM Battery Monitor app), so any quality, standard USB charger of 1.0A rating or higher will provide the optimum charging rate. With your current charger, you charging at slightly of 50% of it's capability.
Note that it does not charge at the same rate all the time, as the battery approaches 100%, the charge rate will slow down. And you can use a higher rated charger (within reason) with no issues, but it will not charge any faster than a quality 1.0A charger.
A standard USB 1.0/1.1/2.0 port will charge at a maximum rate of 500ma (0.5A), and USB 3.0/3.1 will supply up to 900ma (0.9A).
FWIW, I use a Blackberry PlayBook charger, rated at 1.8A, and it works great, but it doesn't charge any faster than an old Samsung charger I picked up and carry in my laptop bag, rated at 1.0A.
The Moto G 2015 (non-Turbo version) does not support any fast charge variant.