It all depends on how far you want to take it and what you want to accomplish. There are many good gunsmiths out there who could do some of the work, parts are readily available, and much of the work you can actually do yourself! About three years ago I was fortunate enough to find an original Navy Colt that someone had taken a file to (restoring?). I have been lovingly restoring it to a worn, but well cared for condition. It has taken time but I have used a stone to remove most of the angry file marks. I had the address line professionally recut on the barrel and a cold blue gave it just the right look.
Going on line I found a guy in Vegas who was able to supply me with an original hammer (the gun had an Italian reproduction hammer when I got it) and a gunsmith friend installed it and fitted it for me. I had the insides rebuilt and then I discovered a wonderful thing, the old girl shoots like a dream! True, the barrel is pitted but enough of the original rifling remains and she can give some good groups. This gun has become my all time favorite.
If you type in "1849 Colt" on your computer search engine you will find, among others, a web site for a company know as "Circle-X" out of Nevada. They will have on line a schematic for your gun, as well as a list of all parts. They can supply parts, original as well as reproduction, as will Dixie Gunworks. The insides can be rebuilt or replaced by any of a dozen gunsmiths out there who specialize in Cowboy Action Shooting gunsmithing. Then, how far you go (factory original, or well taken care of worn gun) is up to you.
My old Navy had so much wear that at the end of the barrel the flats were worn round on the right side from holster drag. To remove that or repair it would have seemed like a crime, so I left that as it ws. A gun that is all original or that might have some collectors value you might not want to touch. But if it is an old, abused, or neglected gun in less than 80% condition then the collectors value isn't there. What I have tried to do with mine is to restore some dignity to the old girl, and remove the scars of abuse and neglect. It all depends on what you want to achieve.