Yes. You can set up a domain-based email (eg info@yourdomain.com) as soon as you have purchased your domain name and hosting space if you want your email hosted with the same hosting company that will be hosting your website. You can also set up an email account with a dedicated email company as soon as you have purchased your domain name if you prefer that but if you keep it with the web-hosting company that you choose, the email account will be free.
Both Bluehost and Dreamhost, for example, offer email accounts with a web-hosting account. Email accounts are free with Bluehost but Bluehost’s hosting cost is higher, so Dreamhost email is less expensive. Dreamhost email is also, in our experience, more reliable.
With your domain-based email, you can use your regular email account to both receive your domain-based emails as they arrive and reply to them from your own domain-based email address.
You can also use a web-based mail platform such as Squirrel Mail or Roundcube to work with your domain-based email account directly and separately. This, however, will give you an additional mailbox to open every day (though you can set up a forwarder to forward the emails to your regular email if you are hosted by Bluehost).