They are versatile. If you like working with hand tools like planes and chisels, then a BS is often the only power tool you may own.
They are pretty much the safest of all power tools. There are only 2 main safety rules: 1 - never push with your hand in line (into) the blade. If you have to do this, use a push stick. The blade don't differentiate between oak and bone... 2 - All work must be in contact with the table at the point the blade hits it. If it isn't, it will be in about 1 microsecond after you make contact with the blade! There is a third one when doing thin resaw as the blade can wander out of the face of the board in certain circumstances so one does not want your hand there either, but that is a less common use unless you are cutting a lot of thin veneer. Push sticks or blocks again...
You can use them for cutting curves and even some scroll work (though extensive or really tight scroll work really requires a scroll saw), as well as general ripping and cross cutting. The downside to some of that is that a BS is not as "tight" as something like a table saw, so you may need to do a little prep work if you want really clean rips or cross cuts. There is a factor with a BS called "lead" in which the blade doesn't always cut quite in line with the fence, for example. A lot of fences are adjustable for this so you can tweak them a couple degrees or so so that they are in alignment and your cuts will be smooth and even, but this takes some time to work on and also can change with each blade you use. if this is critical, you need to use some decent scrap to dial it in prior to cutting the real pieces.
Resawing is the one thing that is really hard to do well on any other saw. 2 reasons for that include the height of the throat opening you can get on a BS for wider boards and also the much thinner kerf the BS blade takes than most other saws. A TS blade is often around 1/8" whereas a BS blade is almost never more than 1/16" and often closer to 1/32". That thinner kerf can be critical in certain circumstances where you really need to get the most out of a board for some reason - even when not resawing. When resawing, the thin kerf is the difference between getting 2 useful boards out of one vs only one, for example.
All that said, I have 2 bandsaws in my wood shop (and a horiz/vert metal cutting one too). One is a bigger 17" Grizzly that is set up for resaw all the time with a nice 1" Timberwolf blade. That one gets the most use by far. The other one is an ancient 14" Delta that I keep a very narrow ~1/4" blade on for curves and other detail work. Rarely used, but a godsend when needed. The resaw is used mainly for resawing (duh), but there are occasionally other needs where it is very handy like dealing with odd shaped things. With only one BS, you can swap a blade and have a totally different tool in just a few minutes. That is where easy blade changes are important.
So a few things to consider...
Enjoy!
-Dave