Pre-hung doors are normally intended for new applications since they include the frame as well as the door. To replace an existing door, you are probably better off buying just a door since you won't have to rip out the existing framing. You will likely need to drill/hole saw for the knob and lock-set and chisel out for the hinges.
The type of door is a personal choice depending on price, insulation factor, look, durability, etc. Your building supply store should be able to help you compare. Installing a pet door would probably be easiest in a solid wood door but can be done in any of them.
Metal is stronger and the most burglar-resistant. Fiberglass won't rot or rust. Wood (solid) is pretty good, wood (hollow-core) is ghastly.
I'd go for the pre-hung door. You won't have to jack with getting the hinges and locking mechanism lined up, it's already weather-stripped, etc. You won't need special tools (like a router). You only need a big enough hole, some shims, and trim.
Hint: Do everything you can to the door before you hang it: prime, paint, install the pet door, prime underneath, etc.
Don't forget to slather buckets of silicone caulk UNDER the door sill before you mount the frame.
I have this dog door, didn't install in a door but I guess you could. Great door and cheap, considering I tried two doors a 40 each that were junk in about 6 months.
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