The weight of the pot is the main issue. Not only is a large pot full of lead heavy, but the grate that holds the pot above the burner will get weaker as it gets hotter. The last thing you want is a pot full of molten lead upsetting because the grate collapsed. So my advice is to plan accordingly.
If you use a large pot, Dutch oven, 1/2 of a propane tank, etc., make certain you have a grate that is strong enough even when compromised by high heat.
When dealing with dirty lead (which I only occasionally must deal with), I prefer an old Coleman gas stove and I keep the weight down. I would rather melt more small batches than one big batch. Unless you're pouring lots of large ingots during one pour, there's really no need to melt all of the lead at once.
If using one of the propane turkey fryers (which are inexpensive and do make lot of heat) be careful not to overload the grate.
The old Coleman "suitcase" stoves are as common as crabgrass and cheap. I think the last one I picked up at a second hand store was less than $10. I burn regular unleaded gasoline in them and I have never had a problem. If an old Coleman stove was to stop working, I've lost nothing.