After you have come up with an offer price, the next step is to determine how large a deposit you want to make with your offer. You want the "earnest money deposit" to be large enough to show the seller you are serious, but not so large you are placing significant funds at risk.
One recommendation is to make sure your deposit is less than two percent of your offered price. The reason for this is that if your deposit is larger than that, the lender will pay particular attention to how you came up with the funds. You might have to provide a copy of a canceled check along with a bank statement showing you had the money to begin with. Normally, this is not a problem, but if you have a short escrow period or are barely coming up with your down payment, it could pose an inconvenience.
Another reason to limit your deposit is "just in case." Although significant problems are the exception and not the rule, they do occur. "Just in case" there is a nasty or prolonged dispute between you and the seller, the less money you have tied up in a deposit, the fewer funds you have placed at risk.
As with practically everything in real estate, there are exceptions to this rule, too. During a hot market there may be multiple offers on the property that interests you. A large deposit may impress a seller enough so they will accept your offer instead of someone else's, even when your unknown competitor is offering the same price or slightly higher.
Since large deposits do impress sellers, you may also find that by making a large deposit you can convince the seller to accept a lower offer. More money up front may save you money later.
There are also times when closing can be delayed by weeks, through no fault of your own. Have back-up plans prepared for such a contingency.