With bigger and more expensive email providers like Mailchimp, you're ultimately paying for higher deliverability.
For startups just getting going with waiting list signups and newsletters, there are a few basic rules to staying out of the spam folder and Promotions tab.
1. Make sure SPF, DKIM and DMARC are setup properly
2. Always "warm up" a new domain and outbound email address
Double opt-in where people have to either reply (highest signal) or click to confirm their email address tremendously helps warm up email. It's also important to slowly ramp up send volume over a few weeks or months and then keep send volume relatively consistent.
3. Consider using a warm up service that auto sends to and replies from an existing pool of recipient email addresses. It can help land your emails in the Primary inbox.
4. Watch out for shared IP addresses that end up on blacklists. If newsletters and emails are important to your biz growth, it's worth getting a dedicated IP address. Just be sure to warm it up properly.
5. Watch out for spam trigger words. Crypto, supplements, etc. It's an ever evolving list of words and phrases that bump up spam scores. Tools like https://www.mail-tester.com/ are useful for checking email config and spam scores.