You should collect at least one month’s rent as a security deposit. In many states, an amount equal to one month’s rent is the most security deposit you can charge. Please re-read the question about landlord/tenant law for guidance. I generally do not like to waive the security deposit. I tell my tenant prospects that it is not a reflection of their economic stability, it is just good business.
If the deposit seems to be a deal breaker, offer to let the tenant pay it in installments over three months instead of all at once. This will usually solve the problem of a tenant with insufficient cash to pay the first month’s rent, security deposit, utility deposits, and moving expenses, all at once. On the few occasions when I do waive a security deposit, I always have a trip wire clause in my lease. It says that the first time the tenant is even one day late with the rent, I have the right to demand a security deposit and declare a default if the tenant does not pay the deposit within ten days.