I don't know which exact model portable you are looking at but I've parked next to RVs with generators installed and they were pretty loud. Take it to heart the advice that running one of these will make very unpopular at any anchorage.
The Honda EU2000
is really what you want. Wise sales online they're about $900, more than you were planning but in this case you absolutely get what you pay for. The Honda
is very quiet and bullet proof reliable.
Regarding the ability to run your AirCon, the only problem you may have would be when the compressor
first kicks in which increases the power draw dramatically. Some aircons may be double or triple the power draw. BUT, this is very short term and if not dramatically over the Honda's constant output rating the Honda should be able to handle the short term startup power.
If not you have two options. You can buy various devices that reduce the startup draw on the generator, either a smart soft start unit or a big power cap. Next option is to buy an inverter
with an automatic power boost feature like the Victron. They can sense the power draw on you generator and temporarily kick in extra power from the inverter
to supplement the generator until the aircon is up to speed. The Victrons aren't cheap
but you will then also have a first class, true sine wave inverter to use for other gadgets.