Hello,

Based on my experience this is one of the hardest decisions when starting a project.

Best case scenario:
- to have a name rather short and domain to be also available (over .com, or if is for a local market maybe something as .co.uk depending on country)
- name must be easily to be spell
- it's optional (sometime even not recommended) to have name related to branch of activity; SEO is important but it's not everything...
- name should be somehow attractive, exciting, "sexy"... let's remember "skype" or similar...

Always are two choices:
- try to find an available domain name
- try to negotiate for a domain you want with a domain owner (who is interested on selling); Is hard to say how much to invest into domains, first choice would be always to try to find a good/decent free option, only if seems to be no option try to negotiate with someone else.

Also, would be good to secure similar domain names (over .net, .info; or if you have a domain as domain.com try also registering domains.com) if are free for registering.

After selecting a name and registering domain would be good to establish branding side: logo, slogan, some graphic guidelines for site layout, aso...