A 77 should have a standard 14x14 hole. If you have the original air conditioner, it might be riveted or screwed to the roof, this is the major hassle. There are several threads describing replacing of original 70's era air conditioners and all the drilling and patching that is required.
The curve of the roof doesn't matter, but you will have to cut some wooden "inserts" that take up the space between the inside and exterior shell so that the new AC has something solid to clamp against. You will need to build these inserts to fit the curve of the shell. The other challenge is dealing with condensate. Your original AC catches the condensate and runs it down a tube that goes inside the wall and down to the bottom of the trailer. There is a condensate pan that is specifically designed to work with Dometic Penguin ACs that can be purchased from dealerships. This plastic pan goes on the roof, and the AC sits down inside it. The pan catches the condensate and channels it down the original tube. Another option that is gaining popularity is a pair of "cups" that attached directly to the bottom of the AC where the condensate normally leaks out, and they run the water into some tubes that go through the mount of the AC and again into the original drain tube. My understanding is that these cups are more "universal" and can be used on a variety of models, unlike the drain pan mentioned above.
As to models, get the biggest one you can afford. You will never regret having too much cooling power. That being said, many people like the low profile AC units just for aesthetics. This will limit your choices--Dometic and Coleman are the companies making low profile AC units that I am aware of. If you truly plan to run your trailer off of a small generator, then you may consider the "low power draw" designs, but note that they offer dramatically less cooling capacity than the other designs, and are not available in low profile.