A lot of IP ranges from cheap VM (and bare metal) providers are included in many blacklists since those ranges were (predictably?) abused by spammers in the past. Some companies are fighting this by denying outgoing traffic to port 25 until you fill a support ticket now, but whatever is in the blacklists will (probably) stay in the blacklists. Even buying your own IPv4 range does not guarantee it was not used by spammers in the past, and you will have to fight the blacklists owners to have it removed...
If you want to be sure your mail gets to someone else, things are going to be more complicated than setting up an SMTP+IMAP server combo, and after dealing with it in the past for work I'm happily outsourcing the pain to fastmail nowadays. :)
Blacklist owners are fairly reasonable. You do need to have an IP dedicated enough that your Reverse DNS can be set to your domain, and then pretty much all blacklists will honor a request to delist it or whitelist it. I've dealt with a couple of them at work.
If you want to be sure your mail gets to someone else, things are going to be more complicated than setting up an SMTP+IMAP server combo, and after dealing with it in the past for work I'm happily outsourcing the pain to fastmail nowadays. :)