<a href=
http://www.labarchive.net>www.labarchive.net</a> and a second just-for-fun site belonging to my husband (<a href=
http://www.waningproductivity.com</a>www.waningproductivity.com</a>) are hosted from my house via a 128k ISDN line. No, I can't get DSL or cable. www.labarchive.net isn't especially pretty, but you can serve a LOT of text-only pages even over ISDN. (Besides, I'm NOT a web designer... I'm a chemist, damnit!)
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I like <a href=
http://www.dyndns.org>dyndns.org</a>. I've been with them since October, and they've been very reliable. $30 per domain for DNS forever is a real bargain. I used dynu.com for a couple months, but wasn't so happy with them. (Reliability issues, mostly.) I'm using ddclient to update my IP address, which changes every time my ISDN line drops. (Maybe 1x per week.) If you want REALLY cheap, you can use their free service (with fewer options) provided you don't mind the name being yourdomain.dyndns.org (or one of a dozen other choices). Dyndns.org also earns big points in my book for not being especially spammy. I think I've had 2 emails from them in 6 months, both of them reasonably relevant.
<p>
Definitely get a router/firewall/gateway/something between your box and the internet. I'm happy to know that nothing but port 80 should be able to get into my home network. Another advantage of a router is that you can give the webserver a static (internal) IP and then only the router has to deal with the fact that the IP address is changing.
<p>
One note on outgoing mail: most cable IPs, ISDN IPs, DSL IPs, etc are listed in RBL or DUL. This means you're going to have trouble sending email directly to some of your users, if their ISP is doing spam filtering based on one of these lists. You'll need to set up outgoing mail to relay through the SMTP server provided by your ISP. It will accept outgoing mail from your IP (of course - it has to!), but many other mail servers won't. And it may or may not mind if your server calls itself www.yourdomain.com instead of uglylongstring.home.com.
