Bill,
Earlier you said it was a Beartooth Bullets kit and later a Bear Basin kit. I am unfamiliar with the latter. If it was Beartooth and you found it too hard, I would call Beartooth and mention it. His sinker supplier may have changed alloys on him without saying so.
Walmart sinkers are definitely not pure lead. At least, they aren't here in Ohio. Instead, they seem to be some kind of pretty hard lead-free alloy and are not suitable for slugging, IMHO.
I mostly use Hornady round lead balls. They are pure lead. I take one that is oversize and roll it between two pieces of steel flat until I have an ovoid that is roughly two to five thousandths bigger than I expect groove diameter to be. I run an oily patch through the bore and wipe the surface of the lead with it, then tap the lead in with a short brass rod.
Goatwhiskers is right that wood is risky to use to try to budge anything inside a bore that's not moving easily. But just to start lead in at the muzzle, it's OK. Brass is nicer and quicker, though, as it's harder and doesn't cushion the mallet blow. Once the slug is in the oiled bore, pure lead can be pushed through with a longer piece of brass rod (best to guarantee you don't wear the muzzle crown) or with a cleaning rod using hand pressure. Some hard alloys cannot be pushed that easily and need hammering through the bore. Don't ever use wood for that, as what Goatwhiskers described can happen. If the bore is oiled and you have to hammer the slug through, though, it's too hard an alloy.
McMaster is at the reasonable end of the price spectrum for
353 brass (hard enough) and I got 3' long 1/4", 5/16", and 3/8" rods from them and as well as a
5 mm by 1 meter long rod in 385 brass for 22's and 6 mm.
For oil I've always used a light mineral gun oil, like Hoppe's, but the next time around I'm going to try the
Ultra Lube 4X penetrating/lubricating oil sold at Lowe's. I've been getting good results using that in locks and on other odds and ends, where it really does seem to be four times more slippery than the usual suspects. It may interfere with bore feel, though, and that's what I need to check. Being vegetable-based, its safe on all plastics and finishes, and that's another reason to prefer it if it works out.