Although some lasers are different, most will engrave anything which is non reflective. For items that ARE reflective there is a special spray paint type liquid which the laser burns on to that surface to leave a black design. My Laser is on the high value side of £20k.
The software for laser engravers/cutters uses different colour lines during the design process, the different colour lines tell the laser to cut deeper, travel faster or slower etc so you can get multi depth designs in a single pass. When I use leather in mine I increase the feed rate of the laser, this eliminates some of the burn that happens on the odd ocasion.
Do you have a specific model in mind? I don't know the cost of laser engravers/cutters in the US, hopefully they are cheaper than over here.