A verbal contract is fine.
I think what you are failing to grasp is that: there is no such thing as a 'low budget client.'
There is simply SCALE. Let me repeat Scale, Scale, Scale, Scale, Scale. Either the scale of what's needed is in line with what we promote or it is not. When our preferred event is one with expensive needs we may turn down events that have small needs with small expenditures.
When an event opportunity is too big for us to handle the price is becomes irrelevant because we lack the skills, staff, or resources to accomplish the goals.
People who try to fake it in either direction are the true source of DJ Horror stories. Pretending to be capable of something we're not while casting blame on others is one such disaster. Another is talking down to a customer about how you''re lowering your self-perceived standards to work with them.
Whether it's $100 or more than $10,000 I treat every customer with the same respect.