You're both right - you don't want to skimp on AC because too small is the worst, but getting one that's too large will cause short cycles and prematurely wear out your unit.
The BTUs needed depend on what type of AC you get - I got a 14KBTU portable to handle four bare bulbed 600s and it couldn't keep my room (fully sealed, 14x10) under 84F with my CO2 generator running, so I needed to get a custom vertical cooltube.
Mini-splits are way more efficient if you're in a legal state or know a cool HVAC guy.
FYI, a good rule of thumb is 4KBTUs to every 1K in lighting (strictly a rule of thumb, your mileage will vary based on many different factors).