A 20 long isn't really tall enough for a veiled chameleon, even a baby. Screen isnt neccesary, but for veileds it works very well. A proper terrarium or screen cage will be the best for a chameleon.
If you are looking for a friendly animal, a baby chameleon might not be the best choice. Some chameleons are friendly, but you wont know until it is an adult. Chameleons in general are not friendly animals (some tolerate handling better than others, and occasionally some appear to seek out humans, but most will not.) A better animal that can be handled and would be suitable for that enclosure would be a leopard gecko or a bearded dragon or maybe a snake.