Hi, I don't think that a different camera is going to be the answer. It possibly could be if what you want is a lower shooting angle (via waist-level finder), but you could have also done that with a tripod mounted 35mm camera. So be careful not to fool yourself about these things.
Originally Posted by kchoquette
Without making this into a novel, I would personally pick out a couple of places to photograph them, where both the background and the light will work out, and start out there. I generally like for someone to be facing into the light, and for the background to be somewhat darker. But there are alternative ways to do everything, so whatever works, works.
I think the most important thing is to interact with the subject, which is more difficult to do when your eye is glued to the camera, or when you are thinking about technical things. So I would suggest to put the camera onto a stand of some sort, and have it preset (you can periodically check the framing and focus). Now you're free to talk with them, make them feel comfortable, and to give directions (don't let them look bad on-camera). Almost certainly this will feel awkward for you - you don't have your camera to hide behind - but I think you'll get better, more "honest" portraits. When the awkwardness eventually wears off, you'll know that you have developed a new skill.
Of course there are other ways to work. Some shooters prefer to let the subject do their own thing while they simply follow and document. (Often this is because they don't know what else to do, I think.) If you are doing this for pay, you may not have time to wait for things to accidentally fall into place. But, like I said before, whatever works, works.