Ok, I just looked a little bit (in the Cabelas Catalog, and the Idaho Regs, which I have).
Your options are limited, but you should still be able to find a firearm that will work just fine. I will point out some options, and possible scenarios.
The regs state that you can't have a scope either, so you are limited to how far you can see to shoot. I am guessing this is maybe 125 yards? I shot my elk this year with a modest load at 90 yards, and that was "pushing it" with the load I had developed, but it worked, and I have meat in the freezer. Earlier in the week, I took a 150 yard shot at a cow and missed, hit WAY low, probably close to 20", but have not actually gone to the range to see where the POI would be at that range in real time.
Another issue is the caliber. The projectile diameter minimum is .428", and your barrel minimum is .50. So, this would allow you to use a sabot, as I see nothing in the regs that strictly prohibits them, except for during the "traditional" season. If you used a sabot then, the bullet would have to be a typical .44 Magnum size bullet, which are .429. FYI - I have a sidelock with a 1 in 48" twist. I can not get sabots to shoot very well in my gun, but I have only tried one type, and gave up, so that is not to say that the gun you purchase will not shoot sabots well.
So, here are the rifles that you have to choose from (assuming that inlines can't be shot with regular percussion caps, which I will follow up on in the blackpowder forum, and ask them in there)
http://www.traditionsfirearms.com/eshop/10Browse.asp?Category=Muzzleloaders%3A+Hawken+%28S ide+Locks%29
The top two there would be good choices. They both have 1 in 48” twists, which would handle round balls and conicals real well. My ML has this same twist and will print about 2” at 50 yds with the load I killed my elk with this year and with round balls.
Thompson Center also makes some fine firearms
http://www.tcarms.com/TC_HTML/TC_Muzzle01.htm
The top two on that page would work fine, as well as the first one in the second row that is stainless steel. They should all have 1 in 48” twists also
http://www.cabelas.com/cabelas/en/templates/compchart/comp-chart.jsp?_requestid=51573
Those are all from Cabelas and should work just fine for any hunting you wish to do. I only marked those that are .50 or larger as that is the minimum for elk in ID. The most common and easiest to get bullets for would be .50 and .54.
As for powder, Pyrodex RS should work just fine for most uses.
Bullets – in the conical (full bore diameter) forms, anything over 350 grains will work. Mine was the 370 grain T/C Maxi Ball in .50 caliber this year. The Hornadys and Buffalo bullets are other options. As for sabot type bullets (if you rifle will shoot them), I have really no clue. There are so many combinations out there that it would take a year of weekends to try half of them.
If you do get a muzzle loader, start with something around 70% of max for your powder charge. You will probably get the best accuracy in the 80-90% range.
Good luck, and also look around the black powder forum if you want more details and specifics.