Which Cartridge Type and Value and best brand around 2000$

Consider including Soundsmith moving iron in your choices

Cartridges | High Output Fixed Coil | Soundsmith (sound-smith.com)

Cartridges | Medium Output Fixed Coil | Soundsmith (sound-smith.com)

Possibly the most cost effective way to own a pricier cart, since rebuild is offered at a reasonable price.

I would go for a moving magnet, and with your budget you can get totl. The most expensive MM cart is the Clearaudio Charisma. It outputs 3.6mV, which should be good for the 46dB setting on your phono pre. I have the Maestro v2 which is fantastic with its boron cantilever and shibata stylus and ebony body. The Charisma has upgraded stylus and tracks exceptionally well. 

You need a high output MC or a MM/MI design—I’d say at least 2.5mv.