It must support the following:
Lots of memory
Member Login (including access to all login accounts by an Administration)
Support
Server Network
My own domain
Instant Activation
All help is appreciated 
PS. What else would I need for a website? It will be a creative writing website, which I hope to expand at one point. Any ideas are welcome, I’m new to the whole website-designing thing
You can’t get a domain for free, but there are plenty of free web hosts out there.
This site lists a bunch: http://www.free-webhosts.com/
free web hosting: http://www.wowebhosting.com/
Try: http://www.110mb.com
there it is,Free Web hosting: http://www.sooot.cn
Give http://vlexofree.com a try.
The server has 8GB of ram, member login, forum support, own server, and you can use your own domain.
Word of advice for your “Instant Activation” requirement is that its a bad idea. Free host with instant activation are usually very limited when it comes to features and resources due to the number of signups they get. VlexoFree Hosting (linked above) manually approves each requested account to provide quality hosting for everyone of their server.
the best place i would suggest is http://www.tucktail.com/ , where i hosted 2 of my marketing sites