Can I get veneers with periodontal disease or at least braces?

If you untreated periodontal disease, braces may create a situation where you will simply lose teeth.  Clean up your situation, start periodontal therapy, and then do braces.  When you are done, you can decide if you ALSO want veneers, but you may not find them necessary.

If you were diagnosed with periodontal disease, then you must have your periodontal disease treated first before ANY veneer or cosmetic work done.  Your canine #11 is in a bad position for any cosmetic work to be successful.  I'm afraid there is no easy way out to get you your beautiful smile without periodontal treatment and braces first.