What should I do? BSSO vs sliding genioplasty vs chin implant? (photos)

I believe you would benefit more from genioplasty and BSSO.  Airway and profile would significantly improve. 

Those are al great options for improving chin position. 
A chin implant is the least invasive way to gain chin projection but it has its limitations. It is hard to gain vertical length and sometimes can also lead to bone resorption overtime. 
A sliding genioplasty is slightly more invasive but offer great flexibility in regards to final chin position and can also help improve the airway. The risk for a genioplasty is numbness of the lower lip and notching at the edge of where the osteotomy is performed. 
A BSSO offer the biggest change and improvement in the airway. However in your case you may need a lefort in combination with a BSSO to help rotate the entire upper and lower jaw complex to give you an ideal chin projection. This would also be the most invasive. 
Ultimately you need to balance what your main complaints are with your current medical conditions and tolerance for prolonged recovery. 
I personally would think both an upper and lower jaw surgery (BSSO + Lefort) would give the greatest change in the esthetics of your facial profile.