What are the most balanced relatively neutral cartridges at each price level ?

What is “balanced,” “neutral,” and “colored”?  There is no fixed reference for any quality, and even if there were, those qualities would be affected by the particular system the cartridge is in.  Even without a reference, I don’t know what you mean by these qualities.  At best, someone can describe differences between particular specific cartridges, but which is closer to any ideal is highly subjective.

At best, you will get different responder's preference at each price level, and not necessarily a preference based on your undefined terms.  I will contribute some of my favorites at or near level 4:

Audio Technica AT ART1000 (recently discontinued at $4950)

Audio Technica AT ART1000X (new model I have not yet heard at $5,500)

Various Ortofon models are certainly good choices, but, it is hard to say that the tonal balance is neutral.  Most of the lineup below the very top cartridges are warmer sounding than average, but does that make them not as neutral?  At whatever price level applies, I like the Quintet Bronze.  I tend to like the Bronze models in each lineup more than the higher priced Black model (Black models tend to be a bit thinner and a bit harsh, although they do deliver extended highs).
 

Again, not having any reference, I would call most Lyra cartridges not as warm as Koetsus, for example, but I cannot say if they are more or less neutral.  I like several models even if they are not as warm as my ideal.  I own an older Titan, although I am currently using a Transfiguration Orpheus L (a slightly warmer cartridge).  If I thought the Transfiguration is closer to the ideal tonal balance, it would be my choice for being more neutral, but someone preferring the Titan would rhink the opposite.

Audio Technica makes an extensive line of cartridges that I think compete well across all of the price levels set out.  As I mentioned earlier, I am impressed with the AT ART 1000 model—not as warm as a Koetsu, but warm enough for my taste and it sounds great to me; it even impressed a couple of Koetsu owning friends of mine.

Perhaps, the different "flavors" one finds from cartridges explains why some people have a large collection of cartridges; some people don't just want vanilla and they like to mix things up.  The cartridges I like don't at all sound alike.  I like the Koetsu Rosewood Platinum Signature and the Audio Technica AT ART1000, both heard in the same system.  I like my Lyra Titan and my Transfiguration Orpheus L even though they don't sound alike.  I've heard, and liked other Lyra cartridges, certain Dynavector and Allaerte cartridges.  For reasons I can't explain, I did not warm up to ZYX cartridges.  I once kidded a friend when I recommended that he get a Van Den Hul Colibri cartridge--it is a very fast and lively sounding cartridge which is exciting to hear, but, I probably would not want to live with it--which is why I wanted someone else to get it so I could play with it.