I am currently a student with no registered business etc
You are required to register (link) with hmrc as self-employed in this case - and while you are at it (assuming profits are below the threshold) register as exempt from Class 2 National Insurance.
Failure to register will result in a fine if (when?) you get tagged...
What is required on a UK invoice is kindly explained by the Government itself (link) which includes the following provisions (copied/pasted for completeness):
You must clearly display the word ‘invoice’ on the document. You must
- a unique identification number
- your company name, address and contact information
- the company name and address of the customer you are invoicing
- a clear description of what you are charging for
- the date the goods or service were provided (supply date)
- the date of the invoice
- the amount(s) being charged
- VAT amount if applicable
- the total amount owed
If you’re a sole trader, the invoice must also include:
- the trader’s name or any business name being used
- an address where any legal documents can be delivered to you if you are using a business name
I'm not VAT registered so does that mean I only charge for my hours *
standard rate and not add 20% for VAT?
If you are not registered for VAT, then VAT is irrelevant... you do not add it to your invoice - although this does mean you cannot reclaim any VAT you are charged on your purchases.
So your invoice value is (as you say)
hours x rate.
If you do become VAT registered, VAT would be chargeable on future invoices (not retrospectively) as an additional 20% of the invoice value.