from which to buy your domain name. A convenient way of doing things is to buy the name and set up the hosting package at the same time, and with the same company.
I look after lots of sites for clients, and use several hosting companies
click here which is a small, friendly and efficient hosting company. They'll handle the domain name purchase for you as well.
click here a much larger company with a state-of-the-art hosting facility. These people are big, ands can offer you everything you'll need by way of service options. Again, you can buy your domain name through them.
You'll find others, but I have personal experience of these two - areti is a company I've known for quite a few years, and although they're small, and not the cheapest around, they provide a very personal service.
Once you've signed up for your hosting package and bought your domain name you'll be able to upload a site to your server space - usually it takes a couple of days or so before the new domain name resolves to the host's name servers, so you'll need to allow for that before you can upload and see your site on the internet.
If you want to make subsequent changes to your site yourself you'll either need to get up to speed with the software that your brother uses to design the site, or investigate the practicality of using what's called content management software - which enables you to upload content changes without knowing anything about site design and /or construction. This software can be frighteningly expensive, although there are some cheap offerings to be had. By and large I would recommend that you hit the learning curve with the design software.
Come back with as many questions as you like.