Go for a Japanese bike. Harleys and Indians are okay if you have a ton of money. A Ducati is super-cool. BMWs are reliable, but expensive. Triumphs are very British. But you get the most value for your dollar with Japanese. There are about half a dozen categories of bikes: Standard, sport, cruising, touring, off-road/motocross and dual-sport.
I learned to ride on a Yamaha Enduro which falls into the dual-sport category. Basically, it was a street-legal dirt bike. This would be a good choice if you like riding in the dirt but need to have a transportation vehicle as well. I ride a standard-class bike now, a 600cc Yamaha Seca II.
Standards are bikes that are not specialized. They aren’t very good in the dirt, they’re not the fastest or most maneuverable bikes, they’re not flashy, and they’re not as comfortable as other bikes. But they do a good job for everyday use. I bought my Seca II new in 1994 and have put 70,000 miles on it. It’s perfect for commuting. I don’t know if the Seca II is still in production, but Honda has the 750 Hawk (and I think the 250 Hawk) and I think Suzuki still makes the 600cc Bandit.
Off-road/motocross. These are toys. Serious toys to be sure, but they won’t get you down to the grocer’s (legally).
Cruisers are the “bad boys”, the bikes you ride for being seen on. These are the Harleys and Indians. There are also several Japanese cruisers. I think the “baddest” cruiser is Yamaha’s V-Max. Gobs of power and “bad boy” looks. It’s a “muscle bike”.
Touring bikes are designed for long rides. The best of them is the Honda Gold Winnebago – er, Gold Wing. A touring bike will get you places in comfort, but I think they’re kinda boring. Still, after a 1,200 mile roud trip on the Seca, I wouldn’t have minded making the trip on a Gold Wing.
Sport bikes are my favourite. Lots of power and razor-like handling. These are not as comfortable as Standards, but they perform much better. All the easier to get yourself dead. You may want to practice a bit before you get a sport bike.
Step one is to decide on the style. Personally I would suggest you get a used standard-class Japanese bike. They’re cheaper, they’re reliable, and they’re good for learning. You may also consider a used sport bike (keep it to 600cc or less), but just think of all that expensive plastic you’ll have to replace when you crash.
Oh, and you might want to take a riding course. I learned to ride on a small dirt bike in the middle of nowhere when I was a kid. I don’t know how many times I fell, but the sand is soft. If you’re learning how to ride in a city, a professionally-taught course is an excellent idea.