I may not be able to help with a name, as I grew up listening to death metal and everything I might post would probably contain the words devil, satan, zombie, or great big boobies.
but, I can say that if you go with a free webhost, the domain name they assign to you will always be longer than necessary. So, save money, go free if you can fit into the alloted space, but register at a place like
dot. tk which gives you a simple address that you can point to your site with, and just give the easy address to everyone.