Welcome to the Forum.
IMO you should be using the gun you have, NOT the Great Plains Hunter.
The barrel on your gun is capable of shooting the slug you mentioned or a patched roundball.
The faster twist Hunter pretty much limits the projectiles to slugs which have several disadvantages. They cost much more than roundballs, they cause greater recoil which is not conductive to accurate shooting and they only beat a patched roundball at ranges out over 100 yards. With Iron Sights, shooting accurately at ranges over 100 yards can be a problem for many (although they won't admit it until you show them their targets).
Assuming you are shooting a .50 caliber gun, a .490 diameter roundball weighs 177 grains and because of its size it will easily take a deer out to 100 yards with a 70-80 grain load of powder.
The slug you mention will also easily take a deer at that range with a similar powder charge.
Speaking of powder charges and because you are new to muzzleloading let me say that one of the first mistakes made is to try to make a muzzleloader shoot like a modern high power rifle.
With this in mind they want to load as much powder as they think they can and then they wonder why the accuracy is poor.
When it comes to muzzleloading, accuracy is everything and a given muzzleloading rifle will have one or two powder/bullet or powder/patch/ball loads which are very accurate so it is wise to shoot as much as you can to find these loads.
These accurate powder loads by the way are almost never above 100 grains of powder.
The thing that is needed is to take your gun out and try several powder loads. Using slugs or patched roundballs I would start at 60 grains (in a .50 cal) and shoot 5 shots at 50 yards. Then bump it up to 70 grains and shoot 5 shots.
I'm betting that 90 grains will be too much and the group size will open up but it is worth trying just to see how well the gun shoots.
As for powders, black is the best by far but it is sometimes difficult to get locally. You have to ask for it at any gun store because they cannot have it out on a shelf like the synthetic powders.
IMO, Pyrodex, then 777, then the "other" powders should be used in that order.
You cannot use pellets in your sidelock with any reliability. Loose powder is the name of the game with these guns.
Before you load, "pop" a few caps on your gun to make sure the nipple/flame channel are clear.
Then, with the hammer at half cock and no cap on the nipple, pour the powder charge down the barrel. When the bullet/ball is rammed the air under it will be blown out thru the nipple, blowing some of the loose powder back thru the flame channel to the base of the nipple.
All muzzleloading guns MUST be cleaned after they have been shot. Even delaying for one day can cause rust to form in the bore.
Also, those synthetic powders that claim to not need cleaning are full of BS. They all leave fouling that will attract moisture and cause rust.
I'm sure you will have more questions and that is what we are here for. We will be happy to answer anything you ask.