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Even a verbal agreement can be a legally binding contract.
In the case of a verbal contract, the difficulty is proving that offer and acceptance took place, and proving exactly what was agreed. The more you leave this 'vague' the more you are at risk.
A signed contract (on paper) is the safest way to protect both parties.
(Obviously you should check the law in your own country)
And any changes or addendums that come up (which you should figure that it will happen alot ;) ) should also be documented and signed off on also.
I would always suggest 50% down. And work out the payments as neccessary. Sometimes this will be a long term relationship with the individual/company that will require a billing every end of the month for services rendered thus far. You may find that you need to write up a contract for the proposed work, stating the 'estimated' amounts etc... Then the 50% is treated as more of a retainer than anything, and you will bill the customer in the stated manner, and at the completion of the project the retainer will be deducted from what is owed. Make sure you cover your bases, you dont want to end up owing some money, and not have it in the bank. :)
Always include verbage for cancellation of contract penalties. And when any of those 'major' changes that the client comes up with last minute that effect the price substantially, dont feel bad about asking for a payment if that amount is 'real' substantial. Just get it in writting with a signature.
Trust me, it will save your butt sometime.