Are any of these tenants on a lease? If so you can't raise the rent until the lease ends. Are you taking over any security deposits? Last months rent? Be sure that is all accounted at the closing!
You got all of this information in writing signed by the seller and the tenants already, right??
Assuming the tenants are month to month with no written lease, you may want to get them on a written lease (even if it is still month to month) so you have something written and you know exactly who lives there and is responsible for what (heat electric etc) also you can forbid smoking (of any kind) and forbid pets, assign parking (if there is any)
Assuming no written lease or MTM agreement, what you do is send them a notice you are terminating the tenancy (if you send it out in March it will end it at the end of April) Then you say if they would like to renew the tenancy they need to fill out an application and sign a new lease (even if month to month) and this is what the new rent will be and raise it on both at least to $900 on the 2 bedroom and maybe $50 on the one bedroom). You can also request a security deposit if you are not holding one (if you want to, you may not want to get into that mess at this time)
Definitely change the locks.
I assume you will want to rent out the other one bedroom? Are you going to do any renovations to the unit before you rent it out?
However, you may want to wait a couple of months, get to know the tenants a little bit, see if they pay on time etc. It might be worth it to keep the rents a little below market and not have a constant turn over.