You will need a domain for your brand, for your website and for business emails.
For Branding, the domain is a valuable asset to the business so a variety of domains are recommended.
I.e. co.uk, .uk, .net
Check this website or others to check if a domain is available by typing in the domain name.
If a domain is not available you could check to see if it is associated with a live website, if not you could contact the owner to ask if they would sell it to you.
To do that, go to Whois lookup too online.
Generally it is one year, sometimes it is two years, it depends on how long it is registered at the Registrar.