Clean Malware and Move OSC website to new server

Hello, I have an OSC website the has malware on it. I have time and time again cleaned the site but it keeps appearing. I have another hosting company which I use that is always clean and always reliable, so I would like to transfer the website to this new hosting company as easy as quickly as possible, so that the client experiences so more downtime and can run the store just like before, with emails etc operating the same.