You've gotten a lot of good suggestions, but I'll add my two cents. I don't know any people that shoot the modern in-lines as target rifles. I'm sure some do, but I've never seen it. It seems to me that those who shoot muzzleloaders fall into one of two camps.
1) They only are interested in the extra hunting season, and the only shooting they do at the range is to make sure they're good to go for muzzleloading season. If that's your interest, in-lines are probably the way to go. Like has been said before, they can be more weather-proof, easier to clean, clear mis-fires, etc.
Using in-lines, you can get saboted bullets, pre-measured pellets of synthetic blackpowder, and the loading process can be very quick that way.
2) The second camp is those who like the nostalgia of real black powder smoke, wood stocks, and playing with all the goodies. Most of these folks hunt and target shoot. This is the group I relate to more. There is something very enjoyable about the process of measuring a charge of loose powder from my horn, greasing patches, casting lead round balls, and even cleaning my rifle that is more satisfying to me.
I would like to say one thing in response to an earlier post about the accuracy of in-lines vs. traditional rifles. It is certainly the case that traditional side-locks
can be finicky, unreliable, and inaccurate. But that's the truth about any rifle.
One thing that is very true about traditional rifles is that cheap ones are not good, and good ones are not cheap. A truly well made and well maintained flintlock or caplock will be just as accurate, if not more so than most in-lines. I believe this is the case that most of the well made traditional rifles are custom or semi-custom rifles that have a lot of care and attention put into building them. The quality control is generally very high and you get really good barrels if you go that route. You can definitely get great accuracy from a factory production rifle (Lyman and Thompson Center are great examples), but if you want top notch accuracy, a semi-custom may be your way to go. As far as reliable goes, there are some tricks to weather-proofing and again, well made rifles rarely misfire if maintained correctly. But there is a learning curve and there is more you have to do to keep them fully functional. It's just part of the deal.
Also consider this. If you use pre-measured pellets of synthetic powder, you only get something like 50 grain increments, but if you pre-measure each charge, you can really test different loads - sort of like reloading for cartridges. Yes, you can get loose synthetic black powder as well. Perhaps this is why I've seen more in-lines than I can count have trouble getting on paper at 50 yards while most of the flintlocks I've seen print clover leaves.
Ultimately, it's about what you want your rifle to do, how much time you want to spend on it, and how much money you want to spend. If you're willing to spend some time and money, traditional blackpowder shooting will make you a much better marksman because it forces you to practice the fundamentals to a level you may never use with cartridge guns. Perhaps this is also true of in-lines, but I don't own one so I'm not sure.
If you're interested in traditional muzzleloading, here are a few websites to check out. They'll give you lots of information and many options as far as guns.
www.muzzleloadingforum.com (a traditional-only muzzleloading site)
www.trackofthewolf.com (one stop shopping for all your traditional needs)
www.flintlocks.com
www.longrifles-pr.com
www.sittingfoxmuzzleloaders.com
Track of the Wolf, Flintlocks, Sitting Fox, and Longrifles all have "kits" available if you are very handy and want to consider building your own. Be warned - these are not like the old CVA kits you slap together. They're more like a box of parts. But they're a blast to make and when you're done you'll have an heirloom quality rifle.
Give 'em a look and see what you think! Good luck!