Only consider using those if they really go along with your name.
If you're planning something that relies on a lot of traffic anything else than .com is risky if you ask me. I'd rather have a longer name and use .com than .net.
Of course if I could get a great, short, catchy .net domain I would. But these days it's not too likely, so the chances are that whatever you're trying to register is already not that great so you can still rename it.
Whenever I see a non-com link it gives me the feeling of it being a B-class website. No matter how un-true it might be that's how my brain works.
For 99.9% of startups anything but a .com is a mistake. How many YC companies do you see getting other TLDs? They're all getting the same good advice.
Buy a good one if you can or choose a name that's not taken.
.me for cutesy personal things, .ly for libyans and .co for columbians. Because of course we have to get our cute puppies, 1.21 jiggawatts of polonium power and some suspicious white powder from somewhere.
Either get them to hold every domain with your name, or for some good url hack. In which case get .com and .net anyway. If I ever get tobyla.ne I'll want to have tobylane.com and tobylane.net.
.com - My first choice but it is tough to secure a brandable domain with 6 chars or less.
.net/.org - To secure it from cyber squatters.
.me/.co - Any projects/gigs related to the startup.
I would get the .net and not give it a second thought. In 10 years having a .me or .ly domain will look like having knee high socks.
.net is still probably far more familiar to most people. Trendy domains are just that. Neat, but may not stand the test of time. However, are domains really even that relevant anymore considering how many will get to your site via a search engine even though they know the URL?