There's is no best inverter air con in the market.

Just like you purchase a hybrid car. Which hybrid is the best to save fuel.
Prius, crz, A6 hybrid or even the high class S400 hybrid.
These are just price difference. There's no such if you bought a car that will never breakdown. Depends how you use them, how often you carry out servicing maintenance.

It's really depends on what spec you need. The function fit your requirements?  Do you need those functions? Different air con comes with different functions etc ionizer, eye sensor, quiet mode bla bla..

Which HP you looking for? 2k budget can get a 1.5hp inverter + installation and have few hundred to get back.

Inverters doesnt cool down quickly. Same goes to other brands. It takes time to cool down the area but once cool down the area. You'll feel the cooling consistent coming out from the FCU which will maintain the cooling by setting the temperature.

At the end.. it still depends on what spec you need.

I will reckon panasonic.