You shouldn't have any problems leveling up by doing all the story quests and the bonus series quests. I have several characters, the highest of which is a 50 Trooper. Basically, I do all the story and bonus quests on each planet, then run as many of the Heroic2's as I can manage by myself before I leave the planet. I've never done any of the Flashpoints, Ops or other large group content. I make sure to explore the entire map (Sometimes you can find quest givers in odd locations). I've only done a few space missions, as I don't care for them. I don't do PvP either.
I've never been too low in level for any area, as long as I follow my class story correctly. In fact, my Trooper was already 49 when I got to Coruscant.
Hope this helps! Good Luck!