The summary.
WHY A CORRECT DNS RECORD IS NOT ENOUGH
The server must also recognise the domain as belonging to an account.
A correct record pointing at a server that does not know the domain gives an error, not your site.
HOW TO TEST BEFORE CHANGING DNS
A hosts file entry. Visiting the server address directly does not show your site, because the request must carry the name.
WHAT SHARING A SERVER MEANS
Mail reputation is partly tied to the shared address, which is why abuse by one account affects others.
WHAT A DEDICATED ADDRESS DOES NOT DO
Make your site faster or improve search visibility. Establish what problem you expect it to solve first.
WHY CONNECTION LIMITS ARE HIT ON SMALL SITES
Slow pages hold connections longer. Improving speed reduces connection use directly.
Hitting the limit usually indicates slowness, not traffic.
CHECK WHETHER TRAFFIC IS HUMAN
On many small sites, bots exceed human visitors. Do not upgrade for traffic that was never a visitor.
WHAT A DELIVERY NETWORK DOES AND DOES NOT DO
It accelerates delivery, not generation. It does not fix a slow application.
SEND MONITORING ALERTS SOMEWHERE OFF THE AFFECTED DOMAIN
If mail fails, an alert about it fails too.