Say my startup is foo.com and I've registered it at namecheap. I'll get a corresponding gmail account (foodotcom@gmail.com) and use that for my outgoing correspondence.
Where you want to impress with your custom domain is incoming email, and in that case, you can set up mail redirects (catchalls in particular) for your new foo.com domain. So if I meet VC Mike at an event, I can direct him to sales@foo.com or info@foo.com. The "handoff" for when I email him back out of the blue from my foodotcom@gmail.com can be a little fraught, but it's good enough until I want to afford actual gmail services or similar.
It's a great way to segment off new areas of your business, so if you hire Vickie in customer service, you can autoforward support@ to vickie@personalmail.mail or vickiefoo@gmail.com, until you hit the big leagues.