I would not advice any company that is continuously being fined for breaking the law.
This is not only an overstatement, it is completely irrelevant. Given the OP problem statement (small business, part-time admin, newbie to mail servers), I do not think there is a better solution A small server already costs 20 USD / month, running a mail server consumes a significant amount of resources, and as the OP mentions running a mail server also represents a high security risk.
Guys, this kind of advice is not helping me either.
First of all, I want to learn how to do it, just for fun. Even if paying for a hosted solution is an economically better solution. It's not for me to decide anyway.
I will not recommend Google. Ever heard of data protection and data confidentiality? And then you are completely dependent. Your are nothing for a huge company like Google. If they lose your complete e-mail database, they will tell you that they are awfully sorry. If at all.
And no, running a mail server does not "consume a significant amount of resources". Any 10-year-old laptop can easily cater for a small business.
Besides, paying $6/user/month is actually very expensive for some small organisations. If you have 20 volunteers coming to the help in a small public library once a month, that would be $1440 a year just for e-mail services. Most such people would continue to use private Hotmail addresses. I would rather install a Synology NAS and use whatever e-mail service it comes with it.
An on-premise mail server is, and should be, virtually free, at least for a basic e-mail service. No need for cloud. No need to expose any ports. No need to configure the firewall. No need to ask anything from your ISP.
I have seen it running like that on existing small businesses with Microsoft Exchange and the POP Connector. It is just that Microsoft wants you to pay a subscription now, probably because the old licence fees are way cheaper than $6/user/month.
If Linus had been reading this mailing list, we would all be paying lawyers to contract professional Sun/Oracle consultants to run our software on certified Solaris servers!
Regards, rdiez