Should I Skip Invisalign and Just Go for Veneers?

Without seeing your case, X-Rays, Photo's diagnostic models, its not really possible to give you any advice on what to do or not do. 

In many cases of misaligned teeth, where someone is seeking a Smile Makeover, orthodontics in the form of traditional braces or clear brace options (Invisalign, Clearline etc) are a great first step. Aligning the teeth means that Veneer preparation can be kept more conservative. 

Generally Orthodontics can align teeth and correct bites but will not change the shape or colour of the teeth. Therefore if all you are looking for is alignment then Orthodontics are the way to go. 

If your teeth are not only misaligned but also an undesired shape or colour then Orthodontics would need to be combined with veneers to get the desired smile. Again, this is case dependant on the condition of your existing teeth. 

Veneers alone, with no orthodontics, is also an option but one that may have some side affects associated with it. If teeth are severely out of line, rotated, or tilted, the amount of tooth removal required, to allow for Veneers, may result in loss of nerve vitality. this means root canals may be needed on some teeth. This is a case by case situation of course, and can't be determined without the help of Photos' X-Rays and Models. 

As far as masking an overbite. It is possible to alter the look of an overbite with Veneers but that depends on the existing dental condition. Length of the teeth, position relative to your lips, etc. Again, different for everyone and determined with the help of the diagnostic aids listed above. 

Talk to a dentist who has experience in cosmetic dentistry and I'm sure they will be able to advise you on both options , Ortho and Veneers, and what would work best for your case. 

Would love to see some pictures to get a better idea of what you are dealing with.