If I were starting from scratch and were in your shoes, here's what I would do:
First, decide what power level you want. Backyard tin can plinking kind of load would require only a simple plain based bullet. If you want more versatility and fear that you might like it so much that you'll be tempted to use it for hunting also, then a gas checked bullet is in order, which would cover all the bases.
Either way, the necessary equipment can be pretty basic (cheap). You seem to have the capability to melt lead so I'll skip that. I would start with a basic plain base mold of around 110-150 grain weight. Scout the mold makers or eBay. It'll be the most expensive part of the whole equation, but no way around it I'm afraid. Next grab a Lee push-through bullet sizing die (use it in your regular loading press) Make it a .310 or .311" diameter- without slugging your throat something that size is a fair bet for starters. Cast a pile of bullets out of wheel weights (old fashioned clip-on style are best), but really for low velocity plinking bullets anything harder than pure lead will work. Lubricate them with Lee Alox Tumble Lube, or stand them up in a shallow tray and pour molten wax-based lube around them to cover the lube grooves, and cut them out of the solidified wax with a cookie cutter-like tool. (A cut off fired cartridge case works fine.) Push them through the size die and voila- done. (Be sure to wipe lube smears from their bases afterwards.)
Next step, load 'em up. You might well get away with cutting a severe chamfer on the case mouths and squeeze them in with your existing seater die. Worth a try. I did it that way for a long time back in the day. Another trick is to make a tool that bells the case mouth a tiny bit, or jam a pair of needle nose pliers in and give a twist- but don't go crazy here, a little flaring sufficient to allow the unobstructed introduction of the soft malleable bullet into the case neck is all you need. Of course you can buy a dedicated neck expanding/flaring die from RCBS or Lyman (and they really are a valuable accessory), but we're doing this on the quick and cheap here.
A slight crimp when seating them will eradicate the case mouth flair.
Powder charge: for a plain base bullet use a pinch of fast pistol powder like Bullseye or Red Dot etc. Something in the range of 5 grains or so will yield many bangs for the buck out of a pound of powder. With a plain base bullet you need to keep velocity way down to avoid leading the bore. Of course, if starting with a gas checked bullet you have a lot more options and can push velocities right up to factory ammo territory. Neat thing about low velocity plinking loads is the most expensive component is the primer. Stand the cases in a loading block and scan the interiors with a flashlight to make doubly-damned sure you don't have a double or triple charge of powder in there. Most important step, for sure. Don't skip it, ever. (50 years doing this and I never screwed up in that regard. It's one of the few things in life I'm truly anal about.)
Once you've worked all this out and loaded a few that work to your satisfaction, then load up 50 or 100 rounds for your next short range plinking session because I'll guarantee that even that many won't seem like enough by the end of the afternoon!
Note: you'll need some added elevation on the rear sight, or a shorter front sight because a low vel cast load will shoot a lot lower, even at "backyard" distances.
Questions re: details to flesh out my suggestions, feel free to PM me.
