Hi,
If you choose to register your business as a limited company, you will need to do so through Companies House, declaring your gross profits and expenses in a corporateion tax return and paying corporation tax on your business profits.
Set up a limited company: step by step
If you choose to be a sole trader, then you need to register for self assessment, as self employed, declaring your gross turnover and expenses in your personal Self Assessment Tax Return (SA100) and SA103 (self employment).
Set up as self-employed (a 'sole trader'): step by step
If your gross turnover is likley to exceed £85000, you will need to register for a VAT account at:
Register for VAT
Please also have a look at making tax digital, as whatever way you choose to run your business, this new guidance will be relevant.
Overview of Making Tax Digital
Thank you.