I have missing teeth and cavities. How would veneers work for me?

Start by gettin your mouth healthy first before progressing to cosmetic procedures. See your dentist for a complete exam and periodontal evaluation. Then, get it done. After your gums and teeth are disease free, then you can start working with your dentist to design a new smile-crowns, implants, veneers. Healthy teeth and gums will assure your financial investment in cosmetic dentistry lasts. 

step1 : tooth coloured cavity filling, step2: restoration of missing tooth > options are implant or bridge, step3: veneers > porcelain veneers for aesthetic improvement.

When a patient is missing teeth, the best solution available in modern dentistry is Implants to replace the missing teeth. These implants would have crowns or bridges attached to them. the remaining natural teeth could be restored with a combination of crowns veneers and tooth colored filling materials.  This is a general answer without having any x rays or photographs to examine.  It sounds like you have been away from professional dental care for several years and a periodontal examination would need to be done with your teeth examination.  Any gum disease and the procedures to arrest the decay should be done at the very beginning of your treatment. Cosmetic procedures and implants should wait until the initial phase is complete. Temporary partial dentures can be made to fill in missing teeth until the implants can be done to help with the appearance of the patients smile.