I can give you a strong recommendation to try Reaper. It's free to try fully featured and has strong midi implementation. You can also try different skins which emulate different DAWs. Ableton is unquestionably the best for composing on the fly ... it lets you run a standard scrolling DAW in the background, capturing what you are a triggering... while you launch "clips" of midi or audio, all time sync'd. Basically a perfect hybrid of DJ sampling workflow, midi notating and DAW editing.
But yeah. Reaper is free. And also great. So there's that.
Thanks for recommendation. Seems that it's very lightweight as it's only 11mb for Win-64bit.
But also looks very interesting.