Welcome. Routers are great for a wide variety of purposes, but most of us at least use them for rounding over the edges of stuff. Makes less easily damaged edges, but also looks nice.. The shape a bit leaves is called a profile, and it's amazing how many profiles are possible given the right bits.
My main concern would be the collet, the thing that holds the bit. Collets are actually precision devices. The difference between a loose, vs tight collet is just a few thousandths of an inch. Here's a picture.
A little rust, a little abuse some time in the past and a collet needs to be replaced. If the bit comes loose, think about having a piece of ultra sharp steel bouncing around your midsection and legs. The biggest problem with old routers of most off brands is that you can't get a new collet because they're not exactly standard, and many of the relabeled router manufacturers stopped making parts long ago.
Glad you didn't pay much for it because if it were me, I'd toss it rather than take the risk. What you'll find if you ask is that there are a few mainstream brands that have great reputations and customer service. Chief among them is Bosch. Others like DeWalt, Makita and a few other brands are also pretty good. I have Bosch routers, and a big Triton in my table.
If you're just starting with routers and want the maximum safety, there are lots of posts about making your own table with a sheet or two of plywood, with a straight board to clamp in place for a table. Bosch makes a special base for the table that allows you to adjust bit height from above the table. A real convenience.
Here's a picture of some roundover bits in a set. These only have 1/4 inch shanks (shafts). If you get a good brand of router with a half inch collet, you can also switch collets so you can use the 1/4 shanks as well. But if you get one of the trim or medium duty routers, you're limited to the smaller shanks, not always adequate for bigger jobs or deep cutting.
Here's a chart with a variety of profiles and the bits that make them.
While I'm at it, here's a diagram of parts of a router bit. Bearings are an important part of your bit selection, but their location, top vs bottom, is counter intuitive.
I've been a DIY guy and done carpentry projects for all my life. Grew up in a beat up old farmhouse, so learned early on. But woodworking is different and a basic set of good tools is pretty important.
I have attached a pdf of a document that describes the 18 or so things that really helped me get up to speed on woodworking. It's kind of long, but has pictures and hopefully, will save you from making some of the expensive mistakes I made. Just don't expect to get all your tools at once, it took me about 12 years of my highest income years, to outfit my shop. I mention it in the pdf, but I have a big library of used and bargain books on woodworking I found through Amazon's used book listings. They were very helpful to me.
