Ok, here you go.
1.) This is a FREE hosting site that allows to you create 5 websites. (I believe that you can use their sub-domains for FREE. They do allow you to use a domain that you would have to pay for as well.) It also has a Site Builder program with templates. Looks like a good place for the new person to start.
http://www.yola.com/
2.) Here is another FREE site that is straight up NO FRILLS. If you are new to this, you will need to do some learning at other places in order use this service. (But it seems pretty robust for a free site. The BIG plus though, NO AD BANNERS required!! A lot of free sites will require you to have ad banners on the pages of your site.)
http://www.freewebsites.com/
I am NOT affiliated with these sites. I signed up for the Yola site, but found a way to get PAID hosting before I actually setup a site with them. I may use them for testing site ideas before spending the money to put them up on dedicated IP hosts.
Space and bandwidth needs will depend on what type of site you are wanting to build. A file sharing site or forum will usually require more bandwidth & space than say a Blog site.
This link may help give you some better answers to your questions:
http://www.gobblerhosting.com/disk-space.php
Domain Name:
Again, the type of site you are making would be a factor here. Buying a unique .com domain that is relevant to your what your site is about is usually your best bet. BUT, if you are just starting out with no money a Sub-Domain will be fine. (You must have SOME type of domain for you site. A domain name is linked to an IP address. This is like your mailing address. It tells people and search engines WHERE your website is. So, to answer your question, YES you do need some type of Domain Name.)
@ the OP, the HD owner uses this site
http://www.handsonwebhosting.com/ according to his post in here. It looks to be a solid reputable hosting site with reasonable fees.
I just found this site that supports BB as well and seems to have a pretty decent pricing plan
http://www.justhost.com/premium-hosting-features (Again, I can GUARANTEE you that I am NOT affiliated with ANY of the sites I posted here.)