How to choose a cartridge?

It is very hard to even begin to recommend something absent some kind of context as to sonic preference and what you are trying to achieve.  It would help to know what cartridges you have heard in your own system or a system you know, and what kind of sound you are trying to achieve.  For example, if we know what you have for gear and what direction you want to move from your current sound, someone can probably point you in the right direction.  If you have heard cartridges that are sort of at the extremes, like a vdh Colibre (fast, clear) and one at the other extreme, like a Koetsu (warm, harmonically dense) and have a preference, that would be helpful too.

I should have specified the Ortofon model—they were SPU models that were quite warm, while the Anna and PW are quite the opposite.

I don’t know if they still offer the service, but vdH use to allow buyers to break in the cartridge then send it back to the factory with a report on what they want changed about the sound; the suspension would then be tuned to try to meet the customer’s specific preference (the service is included in the purchase price).

I,too, think that the Delos is a fine cartridge offered at a reasonable price, provided you are not looking for something very lush and warm sounding.  If lush and warm is your preference, perhaps a Koetsu or Grado or an Ortofon should be considered.

I have not heard the Audio Technica cartridge you are considering, but I have heard the top of the line ART 1000 and it is terrific and not as pricey as other top end cartridges; it makes me wonder if some of their other cartridges are also reasonably priced.

It is quite difficult to audition cartridges, particularly because they are in a system that is totally different from one's own.  I have a local dealer that will allow trusted customers to take home and try certain cartridges that are in the store, but that must be nerve-wracking for all concerned.  I think he even allowed someone to take home an ultra expensive Allaerte cartridge.  So, at best, one hears a cartridge or family of cartridges in familiar systems to get an idea about the sound; after that it is sort of a crap shoot and a matter of making other system adjustments to get the sound right.  

What is "right" might also depend on the music and one's mood.  The truly dedicated might actually swap cartridges or have multiple arms or tables.  I am not so dedicated to analogue, so I stick with one cartridge for a long time, even if I have two quite different sounding cartridges (Lyra Titan and Transfiguration Orpheus L). 

I think you have a very good analogue rig, so it certainly deserves a great cartridge.  At best I can only say I have heard, and liked cartridges from the following brands: Lyra, Dynavector, Audio Technica, Ortofon, Koetsu, Allaerte, and van den Hul.  

I don't know if any particular measurement says anything about how a cartridge might sound, much less whether one will like that sound.  It might well be case, as some mastering engineers have said, that distortions and artifacts inherent to the making of records and extracting the information on records might be what attracts some people to record playing.  I suspect that this, at least in part true.

I once borrowed a table from a shop while mine was under repair.  I noticed that that this setup had a particularly expansive sound field that seems to envelope the room.  I had, at that time, a Yamaha DSP-1 processor that creates multichannel reverberant information to feed to side and back channel speakers.  One setting was essentially a Hafler circuit that extracts out of phase information from the two channels to feed to separate speakers.  When I engaged this circuit, I got a lot of out of phase information FROM A MONO RECORD (with my own table, I would get no signal when engaging this circuit when playing mono records).  The cartridge was not wired out of phase an there was enough in-phase information for there to be a proper center image and proper left and right instrument localization with stereo records.  The amount of out of phase information (i.e., distortion) was not enough to destroy stereo imaging and it may have actually been an enhancement, at least with some recordings.  

Yes, good channel separation will tell you that the stylus is properly aligned with the signal generating elements, that the left and right elements are consistently made, etc., provided you make the measurement on the particular cartridge.  The manufacturer's specification or the measurement of a reviewer won't tell you anything about your cartridge.  Once you buy it, you are pretty much stuck with what you got, so, at best you can try to discern which builders have a reputation for reliability.