Youi will find that you are more limited by what domain names are actually available - this will govern which domain you decide to go for.
There are numerous TLD's that you might want to consider:
.com
.net
.eu
.org
.info
Over the years the very best domains have gone - simple as that.
.com is still the domain extension everyone wants and getting a good .com these days is difficult without splashing out a little.
Same really with the .net domains.
.org offers a few more, .eu is relatively new still and with about 2.5m .eu domains in existence that means there are still some gems to be had.
.info is also popular and lends itself well if you're planning on having a Blog.
You've also got the choice of country level domains.
These are things like .uk, .us etc
A few countries (like the UK) don't sell domains in the top level of their domain space.
So you cannot for example buy a .uk domain.
You have however got the option of co.uk, org.uk, me.uk
co.uk is the most popular, however with no restriction on who can own one and their very low price you'll again find it difficult to find a "good" name left.
org.uk is popular, me.uk is the least popular of the three, however this again means you've got more choice.
The domain extensions you really should avoid would be country level domains outside of where you actually live.
.fm for example had become popular with radio stations, .dj obvious again.
However all it takes is the country to turn around and say they no longer allow outsiders to own a domain and you'll lose it.
Columbia did just this and overnight many owners of uk.co domains just lost them.
new.net also sell domains like .shop, .travel...
These are not true domain extensions, they require software to be running on people's machines for them to work and are a waste of money.
If all else fails there are the more expensive domains like uk.com, uk.net for example extensions.
These are actually companies who own for example uk.com & uk.net and are selling third level domain names.
They are big names behind them, they are legit, but are also rather expensive.
Personally at the moment my main domains:
.com for my main website
.net so I've got the pair, it simply points to the .com
.eu for my e-mail - first name at surname .eu = top e-mail address for life
.info as my alternate e-mail and forwards to my Blog.
It is all really on marketting.
The search engines never really care about what extension has been used, they are far more interested in the actual content of your website firstly and then just who is linking through to your site.
If you've got just a handful of larger sites linking through to you for any reason this almost guarantee's a nightly visit from the bots to catalogue your site and you'll get listed on the merits of your site - not if you decided to go for a org.uk rather than a .com