That's exactly what I would suggest. I am a kind of a ligature junkie, got around 40 or 50... one of the best is the rovner star from my point of view. not too dark, not too superficial (not adding any "own" sound), very easy to handle. same class as a silverstein or a francois louis but much cheaper.Try a Rovner Star Series - hands down the best ligature I've found. Very free and lively. I thought the Rovner I was using before was good, and it really is, but its discontinued and the SS beats it hands down anyway. Rovner has a really good selection depending on what you want to do to your set-up. On tenor I'm always looking for ease of playing, reed-friendliness and a free, sizzling sound. On alto, I use the Dark lig because my mouthpiece is a little bright. A different one yet on baritone. Three different situations with different needs. It all depends on what you're trying to accomplish with your set-up.
You can definitely affect your playing and your sound with ligature selection. I used to doubt this myself but no more. The ligature is just another one of your tools for accomplishing an end. You find one that gets your attention and makes you smile, its like finding a really good reed but it always works.