If you’ve created FPS games, you might as well just go ahead and do it. Unity’s Standard Asset Third Person Controller and camera rigs are a decent way to start. The Asset Store has some good options that are much more powerful should you need them, such as Opsive’s Third Person Controller and ootii’s Motion Controller.
The one technical difference between third person and first person is that the camera is outside the player character. This means it can clip through walls and such. You’ll want a really good camera system that prevents clipping, usually by moving the camera in closer to the player character. However, in really tight areas, you might need to move the camera somewhere else or temporarily hide the player character model to prevent the camera from clipping into it.
The other differences are design-related. First person is more of a “you are there” perspective where the world takes precedence. In third person, the one constant is that the camera is usually focused on the player character, so the character takes precedence. You’ll need to implement smooth motion and good animation for the player character, and allow the player to really connect with the character – for example, customizing appearance (e.g., different outfits) or developing signature moves or actions.
Also, the camera needs enough room to move, so you’ll want to design your levels to discourage the player from spending a lot of time in corners and tight areas.
Sounds like a good idea. All of the paid third person controllers have demos. Try them out to make sure they handle the edge cases such as backing into a corner without camera clipping.