Should I get retroactive effective contract from client?

I have been working with a client from abroad for around a year, during which I built new applications and contributed to their existing projects, also assisting them with short technical tasks. I received payments on a project/milestone basis; should I formalise this as a contract and list it as a contract experience? The client is happy to do it since I have helped them in some crucial situations.

Please guide me on what documents I require to show as experience and how I should formalise it since all the work I did was handshake deals.