Setting up as sole trader whilst being employed?

Hi All, So many videos, so many threads, its just not clicking into place.. Hopefully someone could point my in the direction of "business for dummies" or give me a little guidance on what I want? I am Full time employed. I have also just started a "side hustle" to make extra money to pay for the finer things in life - this being a cleaning business. Customer's have option to pay cash or bank transfer. I obviously want to declare my earnings to the taxman and pay my way for any additional earnings. There is myself and my close friend who have set up this side hustle but want to set up as sole traders rather than a limited company to see how the business takes off. Any jobs I do, i'll take the earnings, any jobs he does, he'll take the earnings, any jobs together we'd essentially split. Some of the money earn't we'd like to put into a "business account" in order to buy new equipment, could we claim anything back on items brought? Where do I start to become official so it's all above board?

Hi Andyjp1,

Please see Working for yourself and also Set up a business partnership: Setting up .  
These links should help you work out whether you are a sole trader or partnership.  
The links within these will lead you into registering for whichever applies to you.  
Please also see Expenses if you're self-employed: Overview  regarding expenses you can claim, including equipment to which you have referred.

Thank you.