I do off-shoot into other areas, but I stay on strength nodes as much as possible. You can totally pick up other attributes to support whatever build you're trying to make, however, they are not necessary. There is gear suited to every class. For instance, there is gear with energy shield AND armour, that requires strength AND intelligence, suited mostly for the templar. Then there is gear with pure armor, requiring only strength, suited best for the Marauder. But since choosing a class only affects your starting position on the skill tree, you can do what you want after that. A big part of the game is skill gems and support gems, and some builds are made entirely around the use of a certain skill. Obviously, to use green and red skill gems, you're going to need the correct stats, but if you don't think they'll be up your alley then it's blue only for you (you can use low level skill gems of the other two, as long as you don't level them too much).
There's also always a passive skill to compensate for everything. For example, as a Marauder, I take no intelligence nodes unless I need to to get somewhere else, so my mana is really low, mana regen is practically non-existant, and I become inable to use my skills after only a few uses due to running out of mana. Solution: Blood Magic Support gem, to augment the skills I desire, OR blood magic passive node to make all skills require health. I have Blood Magic, and can continuously spam a skill over and over forever and never run out of hp. Works for me. For instance, my ground slam costs like 31 mana each use, so that's 31 hp. My health regen right now is 101.2, so blood magic.... *really* good idea.