We've been in our house ('49 vintage) for 10 years. Putting a damper in was one of the first things I did. I believe it originally had a cast iron damper that'd rusted away.

The main thing you need is a cap if you don't already have one to keep the rain out. If that's the case, I'd lean toward a chimney top damper. I put in a Chimalator, and a quick check of prices shows they've escalated to $200+ for the kit from the ~$100 I paid for ours. Price depends on the size.

Honestly, I think the pricing you got is a bit steep for either type of damper, unless you have a massive fireplace and flue and a roof so steep that it'll be a giant pain to get to the top of the chimney.

For the chimney top one, they're going to go up on the roof and put the cap/damper in place with screws and some RTV silicone as a gasket. They'll drop the stainless wire that is used to close the damper down the flue. At the fireplace, they'll drill holes in the masonry for the bracket to screw into the wall. Then they'll attach the wire from above and set up the tension so that the damper is closed all the way when the lever is all the way down.

That's maybe a 90 minute job for someone who knows what they're doing. Marking up the material by 2X to install may be pretty normal. It's also why I DIY most things.