Please forgive my ignorance, as I am far from a photography expert.

I currently have a Canon Rebel Xsi with the package 18-55IS lens, along with a Canon 75-300 (non-IS, from the era before digital). However, I frequently find myself wanting more zoom than offered at 55mm, and I don't want to carry both lenses unless I'm sitting at a kid's sporting event. The result is that I almost always opt to carry a point-n-shoot (Elph, in my case) or (don't shoot me) just use my phone.

I'd like to get a single lens that offers more than the 55, maybe up to 100 or 150. Given my needs and desire to spend money on other things, I'd really prefer not to spend much.

Any recommendations? Also, how important is image stabilization (assuming that is a significant cost factor).

Thanks!