Welcome to the BP Fraternity.
That is a nice looking T/C Hawken you have there.
I like the browned barrel. Gives it "class" and it stands out from the normal (and IMHO boring "everybody and their extended family for several generations has it") blued barrel.
Yes, I hope to brown my barrel in 2020 or 2021 at the latest,
Contact Thompson Center, and request the
'SHOOTING THOMPSON CENTER BLACK POWDER GUNS' manual. (it is in PDF format) it is a more comprehensive manual than the
'HAWKEN' manual (also in PDF format.)
There is no charge for either manual.
Thompson Center only recommends/recommended using FFg (2 F) real black powder or synthetic (faux/fake) black powder like Pyrodex RS grade (by volume. You don't reset your powder measure), regardless of caliber or projectile weight.
For .50 caliber they recommended a .490 patched round ball (using their Bore Butter patch lube, of course) on top of 50 to 110 grains FFg black powder or RS grade Pyrodex.
You will find the most accurate load for your particular rifle somewhere in the middle of those powder charges.
Start with 50 grains and work your way up 5 grains at a time.
Do Not try pelletized powders. They were/are designed for in-line guns, and DO NOT fire reliably/consistently in a sidelock gun. Loose powder, only in a side lock.
You should also be aware that changing patch thickness, patch lube, different brands of caps, and variations in loading pressures can and will affect accuracy.
Swab your bore with a damp patch after every second or third shot when working up loads and sighting in.
When sighting in, use a rest, at least under the forearm. (even if only a rolled up jacket or sweatshirt) That will eliminate or lessen any human errors holding on the target.
Sight in starting at 25 to 50 yards. You want your group a little high at close range. It will drop when you set your target at 75 to 100 yards.
Only shoot offhand after you've worked up the most accurate loads and are sighted in.
In answer to your question: Yes. It takes a bit of range time, powder, patches, balls, and caps to find the most accurate loads and to sight in.
You should also know that
every rifle is different in what loads it likes best. Just because so and so or who and who says "My rifle likes 80 grains best..." does
not mean yours will! - Even if the rifles are the same make and model, and the serial numbers are different by just one consecutive number on the end.
You will probably find your rifle likes a light load
and a heavier suitable for hunting load equally well.
In a .45 CVA "Kentucky" rifle I had years ago, it liked 60 grains FFg for a "target shooting" load, and was just as accurate with a 120 grain Fg (1F) load for hunting.
With either load, broomsticks were an "easy kill". (out to 100 yards with the hunting load.)
(I could see a bit better back then, than I can now.)
You will need a powder measure (the ones with a swivel pouring cone is "best") and a flask.
While not exactly "pretty" an inexpensive brass or plastic tubular flask from CVA or Traditions works just fine.