I'm missing two lateral incisors. What would be the best way to treat it? (photos)

Due to your gap space between your two front teeth, it is best to go through ortho first to correct your two front teeth’s positions. In doing so, it will create some more space for where your lateral teeth would’ve been. Once ortho is done, then you’ll be looking at bridges (not partials) or dental implants/crowns. No veneers to replace your missing lateral teeth.

Unfortunately, orthodontics are your only real answer to correct the your spacing issues. It is possible that a cosmetic dentist (AACD) could correct your problems with veneers, but it may limit their ability to create a beautiful smile without moving the teeth first to create a more ideal alignment. 

Some studies of your teeth and bite would be necessary.  Veneers would be a quicker fix, but would need to do a simulated waxup to see if the new size of the teeth would work in your mouth.  

Orthodontics to widen your smile  is also a possibility , but then replacement of your laterals would be necessary - either implants or bridgework