According to the CompTIA Cloud Essentials objectives and documents, the most cost-effective and satisfying monthly transfer requirements connection method would be Direct Connect (500MB). This is because it has a fixed cost of $200 per month and a transfer limit of up to 250GB, which is enough to satisfy the 300GB monthly transfer requirement. Additionally, it has a lower cost per GB after the transfer limit is reached compared to the other options.

The other connection methods are either more expensive or insufficient for the monthly transfer requirement. VPN (100MB) has a fixed cost of $50 per month and a transfer limit of up to 50GB, which is not enough for the 300GB monthly transfer requirement. Enhanced VPN (200MB) has a fixed cost of $100 per month and a transfer limit of up to 100GB, which is also not enough for the 300GB monthly transfer requirement. Enhanced Direct Connect (1GB) has a fixed cost of$400 per month and a transfer limit of up to 500GB, which is more than enough for the 300GB monthly transfer requirement, but also more expensive than Direct Connect (500MB).