Congratulations.
Your 1861 is a .36 caliber gun so you should be using .375 or .376 diameter roundballs in it.
It will like 3Fg powder best but if real black powder is unavaliable, you can use Pyrodex P or 777 synthetic powders.
Most .36's work very well with 18-22 grains of powder.
Your Uberti will use #11 percussion caps and because of the closeness of the nipple to the powder you don't need to use the magnum style of caps even if your shooting synthetic powder.
If you choose to use a wad, it goes between the powder and the ball. The wad does not go over the ball.
If you choose to use the lighter powder charges you may want to put some filler between the powder and the ball to keep the ball near the front of the cylinder.
If you use a felt wad between the powder and the ball you probably won't need to use a filler.
Most folks put some lube like Crisco over the loaded balls. This will help to lubticate the balls and some feel it reduces the chance of a chain fire.
It is very important that after firing each shot you look at the caps on the unfired chambers.
Sometimes the recoil will jar these loose and if one falls off it leaves an open path for flames from the firing chamber to find their way into the uncapped chamber.
If that happens, you will very likely end up with a chain fire so keep your eyes peeled for this problem.