Buy something used and inexpensive for a starter bike.
Look for something old but not too old. You don't want something so old that it is a junker, but not something so new that you'll feel bad if you lay it down.
Look for something in the 500 - 800 CC engine size. This will be powerful enough so you don't get bored too soon, but not so fast that you will be afraid of it.
Look for a standard or cruiser bike for your first bike. They are more forgiving and usually have less power than a sport bike with the same size engine. Although cruisers are heavier than other bikes they have the lowest center of gravity and are easy to balance considering their weight. Balance is more important than weight for your first motorcycle. Stay away from the sport bikes for your first bike as they require more skill.
Going with a sport bike for your first bike is like getting a Formula 1 race car for your first car, not a good idea. Any decent sport bike can go from zero to deadly faster than you can say "Oh Sh**". Also used sport bikes tend to be more abused.
Consider the fit of the motorcycle. People come in all sorts of different shapes and sizes. So do motorcycles. When selecting a motorcycle consider how well it fits your body. Ask yourself how well you can put both feet flat on the ground. Ask yourself how well the seating position feels. Do you have to reach too far to the handlebars? Riding hunched over can get uncomfortable very fast. Is the foot peg location comfortable? Does the bike feel too big or too small? An uncomfortable motorcycle won't be much fun to ride for any amount of distance. However, a bike that fits you well will be lots of fun.
In general, cruisers will have a shorter seat height than most other bikes. You may want to consider this if you are a short person.
Avoid buying over the Internet. I would never buy a motorcycle sight unseen. You could very easily end up paying too much for junk. Always do a visual inspection and test ride before buying a motorcycle. When you go to look at the bike, bring a helmet. If you do not have your motorcycle license yet, bring a friend with a motorcycle license and 2 helmets.
Watch the classified section of your local news paper. Some locations have shopper magazines with used motorcycles in your area. Reasonably priced used bikes are out there. Be patient. Don't buy too quickly, but if you find one you like, buy it right away. Unfortunately, as the price of gas rises so will the price of used motorcycles. If you find a good starter bike, don't hesitate as they can sell quickly.
Don't get hung up on any particular brand. All of the name brands are about the same. Pay more attention to the bike's condition. If any one brand were really superior to all other brands, this would be the only brand bike on the road. In addition, if any brand bike was really inferior to the other brands, nobody would buy them and the company would be out of business.
Learn on this bike. Make your mistakes on it. You will make mistakes. Nearly all new riders will lay their bike on its side at least once. Would you rather make your mistakes on an older bike or your nice shiny expensive new bike?
The most important thing you should do when getting your first bike is to take a motorcycle safety course.
After you have been riding a while and gain some experience, you can sell your starter bike and get the one you want. If maintained properly and not abused, you won't lose too much money on your starter bike. Put the money from the sale towards the bike you really want. By this time, you will have figured out what style bike best suits your riding style and needs.
Make sure your abilities match the bike before you attempt a side car. These bikes are more difficult to ride as they will not lean in a corner. You lose a lot of stability when you can't lean into a corner.
I know I used variations of this answer before. However, I feel this is good advice.
Use your head while riding. Remember, Stupid Hurts.
Have fun - Ride safe
