Choose a name
This one is tough. Back in the mid 90's this was quite easy to do. Nowadays, the good ones are taken! Not really. A lot of the names are available now. Those who purchased them, have let them expire. You will need some patience and a few hours of time.
Some thoughts on purchasing a domain name.
1. Make sure it is a name that interacts with what your site is about.
2. Try your best to get a short name. Remember, your domain name is part of your email address. Your visitors/customers will like it better by typing in a shorter email address.
3. Manage it. Don't let it expire by accident. You would be surprised at how many people let this happen and lose a name that too a long time to acquire.
Good luck with the hunt!