I've written a number of papers on why pit bulls are portrayed the way they are in the media, and their temperaments as backed by scientific studies, if you're interested.
Pit bulls tend to score higher on temperament testing than many popular breeds such as cocker spaniels, golden retrievers, beagles, border collies, etc. That's not necessarily to say they're better or worse or less or more aggressive than those breeds, but it should give you a good idea of how they stand scientifically and temperamentally, in general, compared to other breeds. Basically, they're just like any other dog, as a whole.
They CAN have tendencies to not get along with other animals, or have high prey drive, as ALL terriers do (some more than others). I find this, oddly, to be more true in the southern US and rural areas. I often hear friends/dog people in southern shelters say that pit bulls rarely get along with other dogs. Up here, most, I'd say at least half, are totally fine with other dogs, and the majority do ok with other dogs when properly introduced.
They are very powerful, and can be large. People will often say they have "locking jaws" or the most powerful bite of any dog or something else untrue. What is true, is that they're tenacious and stubborn, and, again, like all terriers, can be difficult to deter when something is on their mind (like fighting another dog or chasing a biker or something).
They are probably the most popular breed in America, though as most are unregistered, you won't find that in statistics. That said...they aren't a single breed. Most people talking about "pit bulls" are talking about American Pit Bull Terriers, but it also encompasses Staffordshire Bull Terriers, American Staffordshire Terriers, and sometimes breeds like American Bulldogs. A lot of their bad media rep comes from people confusing breeds in things like medical reports, news articles, and shelters. And many pit bulls in shelters are a mix of those breeds, or others.
Because of the above, there is a huge range in their physicality and personality. They can range (as far as general "pit bulls", particularly in shelters) from like 30 lbs to 70 lbs, easily). Some are EXTREMELY high energy with strong terrier tendencies, like prey drive...some are really really mellow and great with small animals. Usually they'll fall somewhere in the middle.
Adult rescues are often acceptable for first time owners, but I would use caution in picking a dog, especially from a larger shelter. Foster care would be good. With a puppy, predict they will end up DA and unsuitable for other animals, or at least have them evaluated by a good trainer beforehand to look for potential signs of DA, and know it's never a guarantee. I've heard people site dogs suddenly becoming DA at 5 or 6 or 10 years old, but I've honestly never seen it firsthand without warning signs. Unfortunately, most people who haven't worked with dogs a lot (and some who have) are unable to recognize those signs.
They can have issues with things like bikes, joggers, skateboards, etc...so that's something to be aware of and provide socialization with.
They love to cuddle and don't usually know how big they are. They tend to love people, A LOT. They're pretty silly and usually if they make you laugh, they'll keep doing whatever it is to get you to keep laughing. They're known to be good with kids, but younger dogs or poorly socialized dogs can accidentally hurt a kid by playing rough (I think that goes for all breeds but people tend to freak out a lot more if a APBT jumps on a kid and grabs their clothes than if a lab does).
BSL is a really prominent issue, so if you rent or ever plan on renting, look into laws in your areas and keep up to date on them because they can change and cause a LOT of heartbreak. Especially with breeds like that, I recommend completing a training class and trying to get a CGC. As the owner of a breed with a bad rap you have an immense responsibility to make sure your dog is an excellent canine example, and be extra sure they never do anything that can be pinned on the breed, like getting into a dog fight at a dog park or escaping and chasing your neighbor's skateboarding kid.
Health issues: allergies, epilepsy....depending on the dog's structure, elbow and hip dysplasia.