Very nicely done for a first effort at woodworking. I'm sure you learned a lot. As piasabird mentioned a good sanding sealer helps condition the raw wood if you are not planning on staining it. You wisely avoided a roller to apply, good call. A good brush designed for urethane is preferable.
Too bad about the original tops, but it is really tricky to sand veneer finishes. Easier to either paint them or start over, like you did.
You can prep the legs with some sandpaper and rattle can prime then paint. Probably would have been easier to do outside though.