Lots of good posts while I wrote my essay below.
Several buckets is going to be a fair amount of lead. Seems like I hear guys saying they get between 100 and 200 lbs of ingots from a bucket like that.
The zinc is an issue. I have been lucky since my source of lead (not wheel weights) never has any zinc in it.
You are going to want to process that lead into bullets in two steps. First, you need to refine the wheel weights (hereafter ww) into some kind of convenient ingot form. You can buy ingot molds (Lyman 4-1lb mold is about $15) but to be honest a cupcake pan works just fine. I prefer the mini size, as they fit in my furnace better. Once you have refined the ww into ingots, you will melt the ingots in your casting furnace to cast bullets.
Refining -
You need to do this outside, as it creates lots of nasty fumes and smoke. Ensure you stand with the wind at your back, so the fumes blow away from you.
When I was starting and still testing the water, I used what I had. A coleman white gas camp stove that was left in my garage when I bought my house served as a heat source for refining. The scrap lead went in a cast iron dutch oven over the flame. I inherited a 3lb lead ladle from my great-grandfather that I used to get the molten led out of the dutch oven. And I stole an old beat up mini cupcake pan for an ingot mold.
You will also need a metal spoon to skim off the dross, and some good gloves to protect your hands from heat. And a flux, which is really anything that will burn and has carbon in it. I use sawdust, left over candles, used motor oil, whatever else is laying around.
Put your pot over your heat source, and fire it up. Add some ww to the pot (maybe a handful). I like to melt about 10 lbs worth to get some molten lead at the bottom of the pot as it aid heat conduction and I feel is speeds melting. Once you get to this point, drop 20-30 lbs (or whatever your pot will hold) in and find something else to do for at least 10 minutes. A lid will also help by holding head in the pot.
As time passes, the ww will soften and get 'crumbly', then will be kinda like peanut butter (creamy), then a grainy liquid, and finally, molten, with a bunch of gunk on top.
Keep the temp below 675°! Zinc melts at about 780°. Keeping you heat below 700° will insure that any zinc you missed in sorting floats on the top. Anything that won't melt at 650° I would get rid of.
Add some of your flux. A tablespoon of whatever you are using is plenty. Stir with the spoon for a few minutes. If you want to can ignite the pot to reduce the smoke and add heat.
The flux causes an oxygen-reduction chemical reaction to occur. Lead-oxide, tin-oxide and other trace metal-oxides form at the top of the pot. These are valuable alloys that are currently in the dross. By adding flux, you present the oxygen a more attractive partner, and it releases the metals to join the carbon.
When you are done fluxing, you will have shiny metal with black dross on top, + the metal clips. Skim these off and discard promptly.
Carefully ladle the hot lead into your chosen ingot form. When I get my pot empty enough I can't fill my ladle again, I add more scrap lead and start over. Repeat until the significant other comes and yells at you for piddling around with your lead.
This brief primer is no substitute for careful reading of the material rcmodel suggested.
Two warnings of significance:
Do NOT eat or drink while dealing with lead. Wash hand thoroughly and often. This keeps you safe from lead ingestion and subsequent high lead levels. I also take 1000 mg of Vitamin C each day, as it blocks absorption.
Do NOT allow water to get into the molten lead. The results are explosive if any what gets below the surface, where it flashes to steam. (This includes drips from a nose on cold days.)
Good idea to visit cast boolits as well. Good luck.