Employers are allowed to require that you accept direct deposit. They cannot tell you where that direct deposit has to go, under federal law. You could request payment by check, cash or a stored value card which you would use like a Visa or MasterCard. I don't know of any law obligating them to pay you in this manner, however.
In many cases, with a little searching you can find a bank that has an account requiring only a minimal deposit to avoid monthly fees and that may be your choice. Savings accounts are often used as well if you don't intend on leaving the money in the account for long. These often have lower costs than checking accounts, but you can't access your money as easily.
Consider in your search how much of your money you will leave on deposit, how you want to access your funds (ATM, debit card, checks, etc.) and what your costs to maintain the account will be. You should also remember that from a personal security perspective, not carrying large amounts of cash will help protect you and your cash. Consider part of your bank fees (if any) some insurance for your well being.
BankingQuestions.com is a free service made possible by the generous support of our advertisers. Advertisers are not responsible for site content. Please help us keep BankingQuestions.com FREE by supporting our advertisers. When you see an ad for a product or service you may have an interest in, click through to learn more.