How to choose a frame to be sure it fits to the owned components?
This is pretty broad, and it depends on how much stuff you want to move over. I'll assume the fork, frame  and headset itself are not being moved, so you're getting new ones of those. 


Brakes: Mounting, reach for rim brakes (can the brake, when mounted, reach the rim properly?)
Wheels: Frame spacing and brakes (if you have to switch brake types you may need to switch wheels). Also, axle type (can't put a thru axle wheel in a regular frame, for example, though some hubs are convertible). 
Stem: Threadless/threaded depending on the new frame. If you switch stem types or stems, make sure the new stem can clamp on the new bar.
Handlebar: See stem. Also, anything that mounts to the handlebar will need compatibility checks if you change diameters. 
Front derailleur: Same type of mount (E-type, etc.). These are cheap though, so replacing them is no big deal. 
Bottom bracket: Depends on the frame. You'll probably end up installing a new one though.
Crankset: Depends on the bottom bracket.
Seatpost: Depends on diameter.
Saddle: Probably will. 
Rear derailleur: Probably will. 


Note that you'll likely be using a shop to move some (all?) of the parts, and at least for prepping the new frame (e.g. chasing and facing the BB and what not).

So, you might as well go through them to get the parts and double check compatibility.