In order to secure my payment term, I am thinking of creating a
contract which will be renewed monthly. Is the contract sufficient or
do I need to get some other proof before starting my work with the
client?
A contract is a legal document. You should never perform any work without having a contract signed by all parties.
A contract doesn't guarantee that a client will pay you, but it gives you legal recourse if they don't.
Can I take legal actions if my payments is not made?
Yes, you can. Again, there's no guarantee that you'll receive payment or win a legal judgment against a client, but you certainly can take legal action.
Additionally, if you don't have it already, make sure that you have Professional Liability Insurance and General Liability Insurance, or their equivalents. These provide you financial protection should a client sue you.