For the email, you can use an email alias service like Addy or SimpleLogin. They're both open-source and offer free tiers. I never give out my real email to anyone now except actual contacts.
After that, I think a VPN would probably still work to disguise what you're doing from Walmart, but I'm not a 100% certain on that so I won't link any.
But yeah, definitely use email alias wherever you can.
I do it with everything. The only people who have my real email address are my family. Everything else is a masked email. It's especially nice because if I start getting spam on one email I can immediately tell which site sold my info and I never use that site again.
I do and it works great! I mostly did this to limit the blast radius of breaches, but aliases also provide an easy way to send those kinds of things to both me and my spouse.