I wrote something about gas below, but first something more important. If you buy an Oxy/Acetylene rig on craigslist *do not* buy one that seems at all banged up. Check the hoses - discoloration from dirty hands is one thing, but if you see any cracks, cuts, or abrasions, pass on the entire set. If they don't take care of their hoses they're not taking care of the rest of it. A small leak in your acetylene hose can kill you, anyone in your house, and maybe some folks in the next house over. The stuff pools at your feet, and if enough of it collects and ignites it can release an incredible amount of energy. Once you do buy a set, leak test everything. Every fitting, the gauges and handles on the regulators, the hoses, the knobs and handle (if you're cutting) on the torch, everything. Acetylene is a really useful thing to have around, but it will be hands down the most dangerous thing in your home unless you're doing something really unusual.
Anyway, on to gas:
For Oxygen and acetylene you don't get tanks refilled, you swap them out like welding gas. Generally only the place where the bottles were purchased will swap them out, though. The bottles will be marked by the supplier. If you buy your own bottles, get them from whatever gas supply is easiest for you to get to.
If you buy the bottles on craigslist, make sure that they're from either a local place that's convenient for you or a chain that has multiple locations in your area (the big ones are Praxair and AirGas). Personally I go to a locally owned shop, since they've been in the area a long time, but the AirGas near me is a perfectly fine place to buy gas. I will say, though, that the conversation is better at a small shop.
Oh, and another option is to rent your bottles. That just means that you don't have to buy them, but every time you get them refilled you pay extra for bottle rental. Even if you buy the bottle, you don't get to keep it - you get a different one every time you pick up more gas.