I've played nine holes for fun once w/just my 7-iron and was +6 b/c I couldn't putt w/the thing. However, it was amazing how often I was in scoring range w/out all the other clubs getting in my way.
In fact, I don't think I've used my driver in a round since doing that and I score much better.
As for putters, yes they can be very expensive for sure. Have your instructor guide you toward which type of putter is best for you and what type of balance you need based on your stroke. From there, I would go find a used one on-line or at a golf store to start w/.
A putter that feels good in your hands is going to save you a ton of strokes on pure confidence alone.
