This list is going to focus on standard and sport-standard motorcycles primarily as they are the most versatile categories, and therefore most useful to a new rider.
Taking rides with friends and even strangers can be an extremely fun and rewarding experience, but it's not something that should be done carelessly. One of the most excellent things about motorcycling for pleasure is that you meet and spot so many others who obviously share your love for the pastime.
In many countries in the world, beginner motorcycle riders are not allowed to ride unrestricted motorcycles. In other words, the bikes are limited in power, allowing the beginner rider to get used to riding a powered two wheeler. Usually after a year or two, the beginner is allowed to purchase/ride a more powerful bike.