The short answer is yes, an oxy-acetylene setup will work for melting PMs in melting dishes. How many hours it will operate for you is of course dependent upon the size of the tanks you select. For the most part, people utilize rental tanks, placing a deposit on the tank and paying for the contents. Probably the most common oxy size is 122 cu ft, which is maybe 4 feet high, and a 2A acetylene. Smaller tanks will not take up any less space to speak of. That same set *could* be used using propane as the fuel, but this will require changing the fitting which goes into the propane tank from an acetylene stem to a propane stem. Not a big deal, maybe a $10 part. They used to be the same. They are not now. Most likely the same *heating* torch tips can be used but the *cutting* head will require a different tip. Again, not very expensive, $10 or so. That you are contemplating a Harbor Freight purchase implies that you'll be getting a Chinese something or other which might not have folks around who can service it....though these things tend not to need service for very long periods. If it's a matter of $20 or $30 extra, I would recommend a Victor or a Smiths or a domestic brand, even used, if they are in good condition. If you select actylene, make sure you have flashback arrestors on the torch. I used to have them at both ends of the hose, probably overkill. Either oxy-propane or oxy-acetylene will melt your stuff pretty quickly, none of this blasting your dish for ten plus minutes. More like 2 minutes or even less.
Be sure to observe tank safety, primarily consisting of: 1: Never having your face in front of the oxygen regulator when you crack open the tank, because if the regulator fails, it can blow the glass from the regulator with massive force into whatever is in front of it. 2: CHAIN YOUR TANKS or take some positive measure to be sure working the hoses does not pull one or the other over and bust off the regulators. 3: operate the acetylene in a vertical position and do not extract more than 1/7th its volume per hour. (that would be hard to do on small melts unless you select a teeny "MC" size tank, a little bigger than a Bernz-o-matic propane tank) 3: Oxy tank gets opened all the way, the valve should be opened up so that it hits the stop in the opening direction. You don't have to super-torque it open, it's just reco'ed that you do not operate the valve in the middle of its travel. 4: But you just crack open the acet tank and if it uses a wrench to open it, keep that wrench right on the tank while you are using it. 5: Be super, super careful of flammable things in your work area, and 6: Wear eye protection and gloves and be mindful of creating toxic fumes...many processes produce fumes, torch heat applied things you don't mean to apply it to (like concrete or regular bricks) can create "explosive" situations, not necessarily flamey explosions, but violent spalling > breakoff of shrapnel-like pieces. Eye protection = essential.
The other thing, you ask will this work "for refining and melting". Yes, for melting. It does nothing for refining. What I am trying to say without sounding condescending is that your ability to melt your metals is maybe 5% of the whole picture.