You have to own the domain before you can do anything. And I haven't heard of any free email hosting providers. If you're going to be using their resources, service and support they're going to want you to pay something. Now, you could get a cheap VPS somewhere and use something like Virtualmin which is a free control panel that can help you set up your email addresses.
Hi your post is a bit confusing there are plenty of free email services
just make a email account like [email protected] buying a domain just to use as a mail service is not really cost effective
When you buy a domain, you will have access to create a business email address but if you don’t want to purchase anything for now, you can use gmail or outlook.
If you want to promote your website it is much better to buy a domain and have your customize business email address but if you will just need an email just to send and respond to normal queries then have gmail for now.