A 50 gallon drum is huge, particularly if you are on a budget. Major expense in making foundries is the refractory. So your aims are seemingly at odds with your wallet.
Since you want to cast 20 lbs of aluminum as a goal, you can do the calculations yourself.
Find the density of aluminum online and determine the volume of 20 lbs of aluminum. Then determine the size of your crucible from that.
When you have the size of your crucible, make the bore of your furnace 2 to 4 inches in diameter larger than that. Give yourself about 6-8 inches taller in height than the crucible is, and that should give you the ballpark for the lining inside dimensions you need. Then add 2 inches minimum for lining thickness. When you've added all the dimensions of bore and lining together, that will yield the outside metal container size you need -- I suspect shorter (and probably narrower) than a 50 gallon drum. But maybe you can cut one down and that might work.
For lowest cost use silica sand and fire clay mix per Gingery charcoal furnace book. It will work fine for an aluminum melter. You don't have to get fancy with additives like sawdust, grog, etc, it works as is. If you want to spend more or experiment with unknown quantities and materials, have at it.
No you don't need insulation, and if you do use it, you will need to support the heavier mass separately from the insulation, and then also encase the fluffy stuff to protect it from moisture. Also you don't need anything thing else, by way of lining additives or coatings unless complexity appeals to you. See my Gingery lathe thread on this forum for what can be done with the simplest 1-1/2" thick clay lined furnace of 8" bore using only charcoal.
For an oil burner, there are millions of examples of every description out there on the net. Pick one, ideally the simplest you can find with high heat output and not necessarily highest temp output and it will most likely melt aluminum in the above. Aluminum wants lots of Btus (calories), but not high temps in a burner.
I've melted and poured aluminum from an open wood fire of pine boughs during a Spring cleanup with no foundry furnace at all. So any foundry with a lining and an adequate burner will do the trick.
None of the above is meant to slight the wonders of modern refractories, high tech insulation, oil burner design advances, hot faces, coatings, etc. It's merely paying attention to your stated needs for low cost and simplicity for a beginner who wants to pour a big mass of AL.
Re crucibles -- I've used cast iron plumbers pots pretty routinely. You will need something bigger. Maybe a piece of 6" pipe with an end welded on -- Better practice than mine would be washing the inside of the crucible with a clay type wash, as iron or steel isn't ideal in contact with aluminum. Or you could spend big bucks on a real crucible -- but again we are supposed to be working within a budget, right? Anything roughly crucible shaped that will hold 20 lbs of aluminum and fit your furnace bore will work, as long as it isn't made out of aluminum or pewter, and if you put a ladle wash in it, should prevent contamination.
My own preferences anyway.....
