I can speak to this from the company law side of things.
If you want to incorporate in the UK it's very easy and takes about 10 mins. You'll need to decide whether you want the company to be limited by share capital or guarantee. Consider shareholdings and whether you wish to use different classes of share. If there are complex arrangements between shareholders this can be dealt with by a shareholders agreement. You can adopt Model or bespoke Articles of Association. If you choose Model Articles I'd
very much advise familiarising yourself with these. You'll need to decide who the Director(s) will be, and a Secretary if applicable.
There are of course tax and reporting requirements. These are more onerous for body corporates than they are for sole traders. In addition to company tax returns to HMRC, there are also filings required to Companies House. Penalties are issued for non-compliance so bear this in mind and keep on top of your paperwork.
As an aside you might want to look into director's and officers liability insurance as well. The cost of defending claims can be exorbitant.
Of course these are just the very broad brush strokes and incorporation is quite an undertaking so I'd suggest taking specialist legal and tax advice at an early stage.
Good luck!