@Yang Zhang I vote or option 1. Get the tenants to sign your contract (I'm assuming they're still on a contract under the previous owner). Explain to the tenant that you'll be increasing the rent by $X amount when they sign the contract with you. However, create value to the existing tenant by making a few, simple upgrades to the unit. The upgrades will make it easier for the tenant to rationalize the increase in rent. E.g. I'm paying $100 more a month, but I got these new appliances-or countertops, or tile in the bathroom, etc.
Ask the tenant what updates they'd like to see, you might be surprised at how little you need to spend. For example, I was considering making upgrades to the kitchen in one of my rentals--would have cost me a decent amount. However, when I asked the tenant what improvements they'd like to see (in return for increased rent) I was surprised when they asked for new flooring in the guest bathroom. This is far cheaper than the kitchen remodel!
Good luck and keep us posted on how it goes!
-Andrew