I heard that some lenses do not work 100% with their abilities on the crop body such as 24-70.
Ignore this. It's bum advice. The issue is that some of what an EF lens can cover is cropped out with a crop sensor camera (the corners), so you are lugging around extra weight that you can't benefit from. However, the portion covered by your sensor will work just as well with your camera as with any other. I shoot with a crop sensor camera, and three of my lenses are EF (that is, OK for full frame).
If you rarely use the 55-250, you avoid one problem, which is that really good lenses in that focal length range are very expensive.
The 18-55 kit lens has pretty good image quality, so I doubt you will see a huge difference when replacing it unless you print large or crop a lot. However, it is weak in some other respects (cheap build quality, very limited ability to handle manual focusing, etc.)
I have only used the Tamron 17-50 that Dave recommends once, but it does consistently get rave reviews. The next longer Tamron, 28-75 f/2.8, is one of my most used lenses. Very good image quality, reasonably good build quality, and a very handy focal length range. Both of these lenses, however, lack usm AF and full-time manual focusing.
My suggestion, however, is that you buy neither until you practice more with your current lenses and get a firmer idea of the focal length ranges that will be most useful for you, given how you shoot. This is a personal issue. For example, I want wide angle for landscapes but longer lengths for people shots, so I cover the short end with a slow lens that is fine for landscapes (EF-S 15-85) and use the Tamron 28-75 f/2.8 as my people lens. Other people want wider angle capabilities with people and opt for the Tamron 17-50, which is much faster than my 15-85. You will need some experience to know which investments make sense for you.