But first let make some things clear. I am not expert so there may be some mistakes. And let me finish first then you can ask questions or give suggestions.

Selecting a host.

If you are really serious about your site/blog always go for a paid host. Paid hosts reliable they provide fast servers. Automated backups for your website and assured uptime.

If you are serious but you cant afford a paid host then there is no option but to go for a free host. While selecting a free host look for one which is online for many years and have good uptime record usually a host having both paid and free services are reliable

Selecting a Domain

Domain is most important factor of a website. Domain represents website so its important to have a very good and stable domain name you can change host but changing a domain is a sign of a bad website so think twice before selecting a domain

There are two types of common domains 1.Top level domain(tld) 2.Second level domain. Top level domain is generally domain name with only consists one dot(.) in it eg. x.com or y.org and second level consist two dots in it eg x.co.uk or y.co.in

Selecting a domain is same as web host paid domains are reliable and free are just free in paid domain you actually own all the rights of the domain and you are the licenced user of it. In free domain you are just allowed to use the domain without any rights on the domain

In fact there are only two free domains I know 1.tk (http://dot.tk) 2.co.cc (http//co.cc). Personally I like co.cc more as its setup options are as good as a paid domain

Setting up a domain