I always look for .com first and in some situation .co.uk. My personal opinion is that .com is the best choice, not only for branding, but also looks profesional and trusted. I don't like all new extentions some of them are realy useless
.com is the most recognisable domain all over the world, so maybe it is the best choice.
Then come .net, .info, .org, .biz and other gTLDs
If you want to make a serious looking local project the best domain is the CountryCodeTLD of the country. And in this case I prefer it.
The ne gTLDs are not very famous and are not recognised by tha audience. And I haven't saw a lot of sites with them since now.