For a VPN to live up to its security and privacy promises, you should ideally have full control over both endpoints of the network.
That is, you want to know that the software on both ends is up to date and doesn't contain bugs and vulnerabilities that can be exploited to quietly leak the data you hoped to keep secret.
You also need to know that both sides are configured correctly, and use strong enough encryption to make cracking the scrambled code to take too long and cost too much to be worthwhile.
Make sure logging, or automated collection of data for the VPN connection is kept to a bare minimum or not at all. Picking a VPN provider or endpoint not in a Five-Eyes country (yeah, that's us in New Zealand) where spy agencies do bulk collection of internet data might be an idea too.
It's also important to make sure that the encrypted data stays that way, and isn't decrypted by a "middlebox" that copy the information silently. You also need to ensure that everything, all the computer traffic, and devices send out a vast amount of data that users don't know about goes through the VPN, or you'll be busted.
Don't forget to make sure the VPN covers both the older IPv4 protocol that used to send and receive internet data, as well as the new IPv6 scheme that is increasingly being used as the number of networked devices grow exponentially.
Done right, VPNs can help protect your privacy and security online; there's no doubt about that. Getting VPNs wrong is easy however so if you have doubts as to how well the one you're using works, don't send or receive anything sensitive.