Not everyone will need a receipt of course, but if you are trading as a business with tax id, then it is in your own best interest to keep good records, and invoicing records are all part of that.
You can issue an invoice via email at the time of confirming a transaction, or you can choose to send a hard copy with the shipment, that's more a process you will need to develop yourself to suit your own operational streamlining requirements.
How To Make One
You can of course use PayPal, design your own if you have the right software, or use any number of custom templates that you can find by Googling the term 'invoice template'
Any invoice with your tax id included will be official.
That's one that you would need to work out yourself really, what is the easiest and most effective way for you to do it. If this is a first time venture then an accountant is always a very good idea.
Should I Have A Website
Well you need some online platform to sell online of course, and an independent website would always be my first choice. Having said that, selling online effectively is about generating traffic to your site, and that's the key issue facing anyone starting their own independently hosted website.
Not the kind of thing I would suggest anyone just starting out should try and take on, it does take some marketing knowledge and some times a bucket or two full of cash to start opening doors of any real opportunity with that choice.
Ebay is of course one of the highest online traffic flow precints around, and despite the fees and what not, still the best place to gain some experience in the filed of online sales in my opinion, certainly.
Terms And Conditions
Yes, you should always have terms and conditions set-out, however just bare in mind that if you are using an avenue other than your own, such as ebay, then any terms and conditions you establish will need to be within the policy limits of the site owner.
Developing your terms and conditions is a matter of how you want the business to run. For example: if you want quick cash flow, then you would be wanting to close a deal asap, so you would place a short deadline on payment, 48 hours, something like that.
That's a term, then a condition of that term could be that any payments not received within that time period will be cancelled and the item resold.
Once again, you need to keep in mind the policies of the site you are selling on to ensure they align with your own or you can find that you have set terms and conditions that you are unable to enforce, and even worse can land yourself in trouble for breaking their own policy!
The location of terms and conditions should always be easily accessible by customers to ensure they are informed as much as possible about what is involved in completing the transaction.
If we are talking about ebay here, then most will have them in the actual listing, but for marketing reasons, people like myself use the ebay 'My Ebay' page to display them, then promote the fact in the listing itself where the terms and conditions are found.
If we are talking about your own site, then you would have a category set aside for them in the menu.