couple considerations and points.
generally multi family (and "diverse" neighborhoods) use mulch, cuz you can't break windows with it.
You can get rock from just about any size from sand up to 8 to 10" cobble. and just about any color. it does absorb heat. It needs weed fabric and the usual suggestion is to lay the fabric one way, then lay another layer 90 deg to it. You'll still have to use roundup and pre-emergent but it keeps it WAY down and generally keeps the roots from getting deep on the weeds. Done forever (minus roundup) and if you get big enough rock it won't get moved by the rain/water off the roof. It will hold heat. 3" of rock cover over fabric is plenty
wood Mulch DO NOT USE FABRIC!!!!!!!! Straight to the ground, it will knit together with ground and hold itself in place as it rots. You need to use 4 to 8 inches of mulch and wet it down (sprinkler) after you finish. (i.e. you'll need more mulch than rock). if you use fabric, it will just knit to itself and when the wind really blows, it will just blow it all off and you'll be left with bare fabric. DO NOT USE FABRIC. Mulch decomposes, you have to keep adding more every couple years. Good news is that it freshens it up nicely, bad news is that it isn't free. You'll still have to use roundup and pre-emergent but again keeps the weeds way down. Will get washed away by big rains. Mulch is ridiculous expensive here (dunno there) but if you don't care about finished look, tree trimmers always need places to dump their mulch/trimmings and it's almost free or minimal charge. Be aware that you can introduce bugs/diseases into your yard that weren't there from doing this. (but free is free). Much cooler than rock but requires maintenance and renewal every few years, also you need literally double the yardage of mulch vs. rock, but you don't have to pay for or put down fabric. Also a wheelbarrow full of mulch weighs WAY LESS than one of rock.