I have an overbite (technically an overjet). I’m 42. Never had braces (Photo)

Your self-assessment is nicely done. What I notice from your pictures is a slanted smile, dark buccal corridors indicating a narrow upper dental arch, gummy smile, posterior crossbite, deep bite and excess overjet. I suspect you have other facial indications that your dental arches are underdeveloped. Underdeveloped dental arches not only cause the dental concerns you have noticed but they can also cause airway and TMJ issues; therefore, just putting veneers on your teeth to enhance your smile may not be the best thing for you from an overall health standpoint.I would consider developing your upper and lower dental arches with simple, comfortable, removable appliances. No surgery is needed. Once your dental arches are the appropriate size to accommodate your teeth then you could use Invisalign to straighten them. This treatment would improve your airway health, give you a broader, more attractive smile and would eliminate your deep bite and excess overjet. It would also eliminate the need to manage veneers for the rest of your life.Good luck! 

I can understand not wanting to go thru surgery at this point in your life! Veneers can definitely help improve your smile, minimize the overjet, and fix the slanted cant appearance. I would also recommend either laser gum lift or crown lengthening on the upper left. This will help balance your gingival heights and overall symmetry. 
I would seek out an expert cosmetic dentist in your area who has experience treating cases similar to yours. Have a diagnostic waxup done so you can have an idea of how your smile can be improved!

Hi:If you are opposed to surgery, there might be a way to improve your smile with crowns and veneers.  However, clinical exam, study model and wax up models are necessary to make that determination.  It’s best to consult with an experienced cosmetic dentist with anti-aging dentistry experience. Best,Dr. Maddahi