It depends on your lifestyle needs and ability to pay upfront. Basic renters insurance policies start with $10,000 worth of personal property coverage, and most people get around $25,000 to $30,000 worth of personal property coverage. If Renters Insurance is being required by the landlord or property management there may be a minimum of $100k in liability coverage however, confirm the liability amount needed in the leasing documentation.
Note that it varies by carrier and some carriers don't offer coverage below $15 - $25K. Also, location can impact this amount: rural vs. city.