Hello Fjorden. I thought I might as well chime in on this because I've got all of the guns that have been mentioned except for a Smith and Wesson Model 3 or First Model Double Action. I just recently sold a Chamelot & Delvigne Model 1873 that was reamed out to .455 Webley. In 2 years I fired upwards of 400 rounds of Fiocchi factory ammo through it and it never missed a beat. I am not certain that the Fiocchi ammo is hotter than the older factory loaded .455 but I have spoken to several people with that belief so I agree. The gun is like the Energizer bunny, just keeps going and going. It still had perfect timing and there were no signs of stress on the cylinder or frame. That is your best option with your budget.
I'm going to mention something that will probably P.O. a few people. I'm going to refer you to a dealer who isn't a CGN dealer because Antiques are one offs, there isn't one of the CGN dealers with a shelf full of that model. Talk to Chris at oldgunscanada.com . He is a great guy to deal with and he won't knowingly sell a piece of junk. He doesn't sell shooters per se, he sells primarily to collectors that are interested in preserving these Antiques, not wearing them out. He has an 1873 for $1,675 that is all there mechanically. It's exterior is rough looking but that's the good part with these ones. Since they were finished In The White, there's no blueing or Nickel plate. Disassemble the gun into it's parts and start polishing with sandpaper or Scotch Brite pads. I took mine from looking like it was found in a bog to looking like a piece of jewellery in one afternoon. Just remember to CLP the finished gun well so it doesn't revert back to it's old appearance right away. So for $1,675 plus tax and shipping and then about $100-$200 to the gunsmith or machinist who'll give your cylinders a ream. So there you would have an Antique shooter that you could fire factory ammo no worries and carry around in a holster on your belt all day long ( in the backwoods of course ) for well under your budget. The On Target .455 ammo from Rustywood is decently priced and nicer than the Fiocchi because it's Starline brass, not the Fiocchi brass with the small primer.
I also have an 1883 model Reichsrevolver that, as everybody agrees, is built like a tank. I think it is peculiar looking , as do many people, so there it gets a lot of haters who've looked at pictures but never held one or fired one. It has no problem with factory .44 Russian or the Rustywood loaded .44 Russian. Admittedly I've only fired it about 80 shots but it feels sturdier than any of my Antiques, actually more like a 20 year old gun than a 127 year old gun.
The French 1892 is an awesome shooter as well with factory 8mm Lebel Revolver ammo. It is hard ammo to find now and those dealers that still have stock are selling it for ridiculous amounts. But it's a fairly easy to reload for cartridge. It is a peashooter and nothing like the .455 or .44 so if powerful was also a criteria then this one's out.
I have a Webley MP that I've shot about 250 times that is still doing fine. But it is such a beautiful revolver that I won't shoot it anymore. Prices on all the Webley models are going up though and you are exceedingly unlikely to find anything close to $2,000 that works properly ( I paid $3,900 for one in Excellent condition ) Also don't bother with the Belgian Webley knock offs. They are great for collecting but not great for shooting. I have an unfired Bulldog clone that, even though it's basically a brand new gun, I wouldn't shoot because it would probably pack it in pretty quick. In their day they were not considered to be shooters. You only fired it when your life was in danger, not going out plinking.
If you are offered a centerfire Colt for around $2,000 I would be very wary. They are beautiful guns but I would think that anything reliable enough to shoot will be north of $3,500. They are like women in that we are dazzled by their good looks and only find out that they're a basket case once you've brought them home to stay. All of the double action Colt's that are Antiques have kind of frail and unnecessarily complicated actions that are quite the opposite of the single action Colt's from that era. I have an 1889, 1895, 1877 Thunderer and a New House Revolver in .41 Long Colt as well as an 1878 in .455 Webley. They all work alright but I wouldn't shoot them because they are too fragile to risk destroying. They aren't making any new Antique Colts.
So there's my two bits on the topic. At least what I can personally attest to. Like I said I haven't owned a Smith and Wesson centrefire Antique yet so I will leave the comment on them for experienced people. I would definitely get one, I just have to get this destructive Colt addiction under control first.
All told, the OP's idea of the 1873 is the best candidate for the criteria he presented, in my opinion.
Cheers all