Is it common to receive first my state tax refund first and then my federal refund later?

The IRS and your State are two separate tax authorities with separate procedures for processing tax returns and issuing tax refunds.  Whether you received one refund before the other does not really indicate anything.

If accepted by the IRS use the federal tax refund website to check the refund status - https://www.irs.gov/refunds

After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions