Although there is no doubt that the Thompson Center and the Lyman Great Plains rifles are amoung the best factory rifles out there, they are in the $350+price catagory.
For someone who has not shot black powder, is on a limited budget and is considering elk, I think I would suggest one of the less expensive rifles for a "first Muzzleloader".
The prices I'm giving are from Dixie, and as is usual with Dixies prices, they can be beaten by other suppliers.
Among the guns that come to mind are:
CVA St. Louis Hawken, .54 caliber precussion. $195
CVA Mountain Hunter, .50 caliber precussion. $225
Lyman Trade Rifle, .54 caliber precussion. $290
Lyman Trade Rifle, .54 caliber flint*. $312
Traditions Hawken Rifle Kit, .54 caliber precussion. $195
Other companies have several other Traditions rifles which are not kits and are in this price range.
None of these guns are what I would consider as high quality. They are basic, reliable guns which are suited for hunting and informal target work. They can give very good accuracy with the right load.
After you buy one, I bet you will someday want a better quality gun, but until you can afford one, these guns will do just fine.
The * by the flintlock above is because I would recommend you buy a precussion gun first.
Flintlocks are a breed unto themselves and while they are great fun, I think just learning the basics with the simpler, more reliable precussion caplock is best.
You might notice I tried to stay with the .54's where both .50 and .54 were offered.
The reason for this is the .54 is fully capable of bringing down an elk if the shot is in the chest. If deer are the largest game you are going to go after, the .50 caliber will be more than adaquate.
Don't be intimidated by the .54 caliber. Black Powder guns offer several things that make this a great size.
First, because it is a muzzleloader, you custom load each shot for what your wanting to do. A 60-70 grain load in a .54 gives about 1450 FPS velocity, and the round ball is about 230 grains. More than enough for deer, and the recoil is actually not bad at all.
Going up to a 110 grain load will push the velocity up to the 1900 FPS area and will take elk.
Second, Black powder does not kick like modern smokeless powder guns do.
Rather than the sharp, stabbing kick modern cartridges give, black powder, even in it's hottest loads is more like a giant rapid hard shove. Of course if you shoot the heavy slugs available, this shove can be somewhat unpleasent but with round balls, it is no problem at all.
Third, the .54s just seem to be inherently accurate. I'm not sure why, but my .54s always seem to group better than my .45s and .50s.
Speaking of round balls, they will kill just as effectivly IMO as any of the modern bullets if the range is inside 110 yards.
They also cost a LOT less, so you can shoot a lot more without going into debt. (Last I looked, a box of 100 .530 balls for a .54 caliber gun ran about $13 (Dixie price). Slugs on the other hand are in the $12 for 15 bullets price area.
Buy a muzzleloader. It is a enjoyable adventure into a world which is such great fun you may find all of your other guns gathering dust in your closet.