I want email to arrive to my inbox without problems, not too ambitious I think?

What I have:
* several free emails, among them only gmail works perfect
* separate server (Cpanel) with my own domain, I have an email set there
* plenty of domains and servers, enough capabilities to cover email needs of a small city

What works:
* free gmail works perfectly
* other free emails do not work too good
* my separate own email server works rather poor for some reason
First, I would like my own mail server to work, this should be the easiest since I have almost full contol of it, correct? It is Cpanel shared host, the domain is setup as full A record (no separate www/MX, both on the same machine). Probably, I would need to change some settings?
Next, I would like more gmail accounts (one won't do

), do you know if they allow more accounts? Or some affordable commercial ones? Any solution to have more of them (but do not be in danger of being banned due to some ToS violation, this would be reallllly bad).
Do you know of other good free/commercial email provides other than gmail?
After I have these I would prefer to get at least one of the free emails to be used as my own domain, I mean I heard something about a gmail offer, you can use the gmail but it is shown as your own domain (like everything send to
admin@lordsgame.com would end in gmail account, and everything sent from the gmail would be shown as my email).
Bear in mind that my email knowledge is rather poor, so posting also theory, lenghty explanation of basics and such are highly welcome 