I need some helpful advice on what amp I should buy.

My set up currently consists of an Ibanez Art100 (bridge and neck humbucker), and a Boss Turbo-Distortion (DS-2). I also have an Ibanez GIO (basically a strat with the pointy Ibanez head-stock and a humbucker in the bridge), which, though it came in a starter set, I absolutely love.

I'm looking to replace my amp; a 15-watt Ibanez brand amp that came in the same starter set as the GIO. My main issue is it has a really, really shitty distortion/gain/overdrive/whatever sound, especially with the Boss pedal. I had a Line6 Floor POD, which sounded fine with it (because I guess it basically overrode anything that the amp tried to do lol), but seeing as it's not quite the same in basically any regard as the Boss pedal, a change needs to be made. Keep in mind, at the moment I'm really only playing in my room, so any perception of how it would sound in an area larger than a 15'x17' room is totally absent.

I'm looking to get a sound close to that of Asking Alexandria/A Skylit Drive/Senses Fail/etc. Like a big, solid, tight low end, but with the high end still really clear and not engulfed by the bass. What amp brand/series do you all suggest I get? I have absolutely no idea what my budget is like, so if you can throw me a wide range of prices/sizes, that'd be beautiful.