In order for the emails from the contact form not to go into your spam folder, you should send the emails from an address of your own domain and add the email address of the customer as a Reply-To header.
As for the emails from your domain arriving in you customer's inbox, you should have SPF, DKIM and DMARC records set up for your domain ( https://www.cloudflare.com/learning/email-security/dmarc-dkim-spf/ )