An annoyance with MTG

In Magic the Gathering, I find my favorite tricks are card draw and mana acceleration. Unfortuneately, these will not win a game by themselves, so I often struggle to build an effective deck that I like. One thing that makes it especially difficult, is that I don't like using counterspells, and counterspells seem to be the most powerful aspect of Blue. So it's like playing with a major handicap, doesn't lend itself well to fun when playing with strangers.