fireplace door and stone veneer over brick fireplace
For those who came here from web search, I've done this and I can share my experience.


You install doors before.
There will be gaps between firebox bricks and door frame - cover them with cement.
Remember to raise doors high enough over existing opening to allow for the thickness of the new hearth stones (if you plan to put them) so that these little vents in the bottom of the doors have unobstructed air flow
If you plan to install stone veneer with corners build up a wood frame over bricks deep enough to accommodate these corner returns
Cover all the gaps with cement
If you built the wooden frame, you don't have any metal to put cement on. It's all covered with plywood and wire and cement layers.
If you had a mantle shelf you might need to redo/rethink how you want to secure it after the stone is laid, but before actually laying the stone.
Instructions call for cement type S ($7 per 40lb), but my experience shows that you need  much more experience with stonework to use it than I had, so just use polymer modified tile thinset ($25 per 40lb)
Use cement type S + cement colorant for grouting
Forget finding the perfect stone, cut and cut and cut 
Get yourself a vac enabled cover for angle grinder and use shop vac