Welcome to the world of local government Helen. As Graeme has said, sit down with your council's standing orders and read through them. If they are based on the national model, they are a bit daunting and many aspects will not apply to a council as small as yours, but they provide the framework. I can also recommend the Good Councillor's Guide, which you can download from the web and provides a common sense plain English guide to local councils.
In terms of the specifics, it is best practice when making payments to have the invoice and chequebook together, so that the signatories may examine the item of expenditure, then sign the cheque once approved by the council, initial the invoice to show that they have verified it and signed the cheque, then initial the cheque counterfoil, again to show that they have authorised the payment.
If you are paying a member of the council to serve as clerk, this is not allowed. Members of the council cannot be employed as officers of the council.
There is plenty of training available and training sessions provide an opportunity to meet with councillors and clerks of neighbouring or similar councils, as well as asking specific questions relevant to your council.
Finally, there is a perception that parish councils have an important role to play in the planning process, but the reality is that we are just one of many statutory consultees and our views are frequently overlooked.