I've used TSOhost and 34SP in the past. Both I find are reliable webhosts and are both UK based which can be handy should you need to contact tech support.
If you are simply registering a domain name for future use (so what may be called Domain Parking), then you can use anyone to do that, though check conditions about transfer of domain - such as any fees involved with a transfer. You may transfer the domain in future to whichever company provides your website hosting.
With regard to webhosting... your website designer (such as Zoe and her team at BWebsites) will be able to arrange that, or you could do it yourself. Some webhosts will provide template based packages to create your own website... can be good initially though anysite based on a template is going to look like another site based on the template.
Your business idea may involve quite a complex website... it may need a shopping facility, order tracking.
I would suggest you think about if you are going to be able to design a website yourself, or if you are going to use a designer... then take things from there. Think about what functionality the website would need to have - is that something you can code, or something that is already provided as part of a package. Does your website need to be Tablet / Phone friendly? Would you need it to be findable easily by search engines. How good are you at creating images for the website... logo, pictures, backgrounds, all sorts of things may be needed depending on what it is you are wanting to do. Lots of things to consider... along with Budget.
You could send an enquiry to a webdesigner with some basic details of the concept... and see what they suggest.
Personally, having created websites myself over the past few years, for something business related I would use a webdesigner, as quite frankly I have not got the time or the energy to be coding things myself, fiddling with code to get it to work on multiple devices/platforms. I would use a content management system, so that the site could be created but have thing updated by me - in a similar way to editing a post on Wordpress.