Welcome to the forum. You can get roundover bits almost anywhere, here's a picture of a Freud set with 1/4 inch shanks (shafts). The bearing rides against the edge you're rounding over, so of you have thin stock, you might use double sided (carpet) tape to add a second board under the first, even with the edge you're routing so the bearing has something to ride on.
Second pix is of a router mounted on an edge guide. You can use a small (trim) router for a lot of different cuts, just don't take off very much at one time. The guide would allow you to cut a groove or dado in many small (1/16th or so) passes without wandering off the line. Not sure if your brand router has that accessory available.
As you get more serious about woodworking, consider getting a Bosch 1617 EVSPK, which is a kit with both fixed and plunge base. You can use the fixed base to mount in in a table (safest way to work). The Bosch has an amazing array of accessories including a really top notch edge guide that will also help you cut circles.
Sounds like you might be starting into woodworking, so I've attached a pdf of the 17 or so things that helped me accelerate the learning curve. It may help you avoid some of the costly mistakes I've made. If you aren't wearing a dust mask whenever you work with the router or any other tool, go get at least one of the 3M masks and always wear it. The really fine sawdust, once in your lungs, never comes out. COPD and restricted breathing is no fun.
Ditto to Dan's comments. The height of the bit makes the difference in the appearance of the cut. The drawings with the bits show what it looks like with the bit set pretty high, it leaves a flat above and below the roundover. Lower the bit and the flats go away.
