RE: Thompson "New Englander"
The Thompson Center New Englander is a meat and potatoes rifle. Maybe not real fancy, but good shooters. They have a 1:48 twist barrel which means they will shoot roundball and conical bullets as well. They use a #11 percussion cap to ignite the powder charge.
Since your rifle is a .50 caliber it will take a .490 roundball and .015-.018 lubed patch. I would suggest starting your powder charge at 70 grains then a patched roundball. Start shooting at 25 yards and shoot for groups. If the groups are tight, kick the charge to 80 grains and even 90 grains until the group starts to fall apart.
If you give Thompson Center a phone call they will send you a manual that will tell you a lot about your rifle, how to clean it, and what loads it likes.