I need to set up my Magento so that all new customers need to get approved.
Once approved I will assign how they pay.
Some pay immediately
Some get a monthly billing cycle
Some will pay by cheque
How can I set up the account approval
How do I assign the different payment methods to their account when approving them?
You can setup customer approval in Admin -> System -> Configuration and in that you can see the option in customer tab.
For other you need developer who can customize as per your requirement.