From what you want accomplished to make your business as automated as possible, then getting a billing system is the best bet. For ease of use, I would go with either Client Exec or WHMCS (which is what we use) and takes care of most the automation you need including monthly payments for existing clients as well as setting up a new account after payment is recieved.

However as noted earlier, I wouldn't allow instant sign ups even with fraud protection in place like MaxMind which is highly recommended to have. It is MUCH better to look over each order as they come in and you determine if it is real or not. If you have any doubts contact them and see what kind of response you get. Fraud is a constant problem with online businesses, web hosting is no exception and you want to make sure you reduce as much of it as possible as chargebacks etc can be costly and take a lot of your time to deal with.

Payment processors, most billing systems allow you to use a wide range of processors to bill your customers. Most of them are easy to sign up with and use, but what you have to compare are the rates each one charges etc. Paypal is always easy to setup and you get a near merchant account. Been using CDG, and they have been good to deal with.