Or is there anything else?
No reason to do either – just invoice, fill out a self assessment form later down the line, pay whatever’s due. – which may be little or nothing if your earnings as a whole remain under or close to the threshold. If this extra work will all be over the threshold (ie all your current PAYE to date has used up all your allowance, then the tax bill on the extra work will feel comparatively sore, but as a percentage of all your earnings it’ll be very little really and compared to the costs, responsibilities and bother of setting up companies or whatever, half and hour of form filling and keeping a few bob aside is easy enough
There would only really be any merit in looking at Limited company stuff if the threshold you were under was the Higher Rate one – or rather because you expected to go a long way over it