There are three levels of email professionalism:
1. Personal: firstname.lastname@example.org
2. Off-brand: email@example.com
3. Branded: firstname.lastname@example.org
Number 3, a branded email, is the only acceptable option. Your email address should use your own domain, not someone else's. The legitimacy it provides is well worth it.
List your email address in the header and/or footer of your website - these are the first places that a visitor will look. Your Name, Address, and Phone should be listed on footer of each page. Sharing your contact info prominently helps visitors feel welcome.
A note about forms: This tool can be useful, but should not be the only way to contact you. Customers cannot always track their communication with you via forms. As a courtesy to your visitors, list your email and use forms as a supplement.