As Josh mentioned before me, I am not aware of any minimum money requirement to make a contract legal. Contracts are agreements between persons or legal entities (e.g. - corporations), in which one party agrees to perform a service or provide goods in exchange for the payment of money or other goods or services.
To be a binding and legal contract, there must also be an offer and acceptance that involves the exchange of promises to act and/or provide goods, services or money. The act, promises, goods, services and/or money are called “consideration.” In order to have a binding, legal, enforceable contract, there must be consideration and promise to pay by a certain time frame.
Looking at a Florida Bar Realtors Contract for Sale and Purchase, earnest money or a deposit can be made / delivered in 3 ways. (1) Accompanying the offer (2) Made upon Acceptance / Effective Date (3) Made within X amount of days after Effective Date. Earnest money however is not required; nevertheless, a consideration of some amount certainly would make an offer more appealing to a seller over one where there is no earnest money which essentially shows good faith.