Never had a L lens. heard its too good to have one.
When you start thinking like this, stop. Yes, the L lenses in that focal length range (there are a bunch of them) are all very good. At least two of them are truly outstanding. However:
A 70-200 L with IS will cost you MUCH more than twice as much. The 70-200 f/4 IS costs about $1300.
More important, for most purposes, unless you are very experienced, you are not going to see a huge difference in image quality. I know; I've owned both the 55-250 and the 70-200 f/4 IS. Until you have a lot of experience, most of the variation in image quality will be you: how well you compose the shot, how well you choose settings, how carefully you use the various AF options, and how well you post-process the image.
So I am with most of the others: get yourself a 55-250. It is an inexpensive lens, and it feels like it, but it can take very good images, and it is an excellent lens for the price. Then practice a lot, and when you get to the point where that lens is holding you back for some reason, consider upgrading.
And when you do get to that point, there is nothing magical about L lenses. There are lots of superb lenses that are not Ls, and many of them are much cheaper. I have been shooting for decades and currently have 5 lenses, of which only 2 are Ls. When you get to the point where an upgrade makes sense, shop around and ask for specific advice here. In some cases, you will find good, much cheaper options; in other cases, you may not.