Different bits cut different profiles. Here's a guide. I think most of us could use a set of three roundover bits as a very basic set. I added a picture of a set.
Here's a chart of profiles and the bits that make them. Worth printing out and keeping in your shop.
You can do some very complex profiles by using two or more bits. For example, I make picture frames for my wife's paintings (she's pretty good), but I like the frame's outer edges to be raised high, but still need to cut a rabbet deep enough to hold the canvas and stretcher. With a fairly thick piece of wood, I can cut the profile such as the bead and cove, then use a rabbeting bit or a straight bit to cut a 3/8ths wide, 5/8ths to 3/4 rabbet into the squared inside corner. That gives a really nice profile that makes an attractive frame that finishes well.
I tend to buy bits as I need them, and for grooves and dados, I almost always prefer to use a mortising bit and make several passes. One of the most useful things in woodworking are jigs, things that hold the tool and allow you precise control of the bit. One of the best jigs to make is a 26-28 inch exact fit jig. Here's a picture:
You fit the shelf you want to fit into a dado in a bookcase, for example, then close the movable jaw and lock it in place. Then your router bit with a "top mounted" bearing, rides against the gap first one direction, then the other. You make three passes, about 1/8th each, which gives you a perfect dado. A groove is the same, except it is stopped, and doesn't extend all the way to the edge. Here's a mortising bit I like, with the top mounted bearing. I like it because it cuts a very flat bottom, important for maximum glue contact.
Here for your info is the location of top and bottom bearings.
There are many specialty bits. For cabinet makers, there are door and face frame shaping bits where you use three or four bits in succession to get a profile in a style you like. I have two sets, one of which is for cutting a groove for glass. If you are into making boxes, there is a very fancy Lock miter bit that makes an interlocking shape at the end of each side of the box. It is tricky to use and I use a little commercial jig to set mine up. Very precise! Huge amount of glue surface.
So, as you can see, there are a huge number of specialty bits, and the one you want is based on what profile you want to cut. I hope this is helpful. I know it took me awhile to learn this stuff, and a fair number of mistakes.