The Canon 18-55mm lens is a "kit" lens; it has a plastic mount (the part that attaches to the camera) and is normally sold with a camera to get people started. It is not a terrific lens, but it does the job.
I have a Canon Rebel, and I went down exactly the path you're talking about. My Rebel came with a 18-55mm lens, and I already had a 70-300mm lens from my daze of using a Canon film camera. The small gap between them didn't really bother me (I do have feet), but I got very tired of switching back-and-forth.
Recently I got a (slightly-used) Tamron 18-270 lens. I have limited experience so far, but it seems to focus OK on moving targets - always a major issue for me (sometimes I take pictures of NS trains that move
a lot faster than CATS trains do) - and frankly my eyes don't see any difference from the kit lens that it replaced.
Of course, you could always follow the path used by Roger Hogan, Jerry Day, and others, and buy $$$$ professional-grade lenses, but it you don't/can't follow that path, I believe that Tamron and Sigma lenses are just fine.