For personal email, should you use a custom domain?

I've used both. It depends on how personal your personal email is. A custom domain is only worth the expense and trouble if your email address is in any way part of your first impression.

If you are just giving this address to the services you sign up for, friends and family then GMail/Outlook's reliability actually make them preferable to setting up an email server on your domain.

Fastmail et al sell their paid service on a promise that you see no ads, and the contents of your emails will not be scanned by the same automated services that Gmail/Outlook use. This doesn't translate into better sending/receiving of email and depending on who you are, you can decide how much that extra privacy is worth in terms of dollars.

> a free service like Gmail or Outlook

Do remember that for "a free service" that you are not the customer, you become the product to be sold to advertisers in that situation.

You also become subject to the whims of "the free service". Should they decide to "alter the terms of the deal" you have only the options of "pray they do not alter them further" or "leave". And as to whether you can extract your data so you can "leave" intact, well, that is one of those deal terms where they set the rules, not you.

It makes it a lot easier to move to a new provider and looks more professional.

If you have to, you could use a custom domain with Gmail.

I use a custom domain with Fastmail.