Re: Fixed IP?
For preference, a fixed IP is going to be best, so that messages can be delivered over the internet directly to your mail server.
However, if your concern is more about, for example, having your own IMAP store so you can find any messages you want, then you could add Fetchmail to the mix, which will grab messages from external mail accounts and feed them into your server. You'd then simply ensure the server has a fixed IP on your local network, which your own clients would connect to (and perhaps use a dynamic DNS system if you want remote access). Outgoing mail would, in that scenario, probably be routed via your ISPs mail server.
A fixed IP will certainly give you much more flexibility, and that's what I have - in fact, I have a routed network on my ADSL.
I don't generally have problems with messages being rejected, because the IP range is allocated to me; ok, it costs a little more than a bog standard domestic broadband, but I work at home and figure it's worth it.
For ISPs that will make this easier, I suggest you check out the article (and the comments) that I did earlier this year about "Boutique ISPs".