Later on you may be buying individual bits, I like many of the brands posted above, but most often wind up with Freud bits, which are easy to find at Home Depot or at Rockler (the only woodworker supply anywhere near me). I also especially like sets from Sommerfeld tools. Pricey but highest quality.
BTW, Marc Sommerfeld has a series of videos on YouTube that are really good at showing basic router technique. Remember when watching that the safety guards have been removed so you can see what's happening in detail. But keep your guards, featherboards and other safety devices in place as much as possible. It's nice still having all your fingers when you're old.
The Sommerfeld videos feature his products, which are excellent, but he was a cabinetmaker for years and his methods are really good examples of doing things in the simplist ways and getting good results. I have three of his door making sets, where you use different bits to make different parts of the cabinet, the doors in particular. Freud also makes many of the same sets.
There are a lot of YouTube videos out there, but not all of them show good methods. But I'm sure you'll learn to spot the difference pretty quickly.