Advice on best mid priced MM cartridge choice for Rega P3 (2016)

Check out the Hana line of carts. I’ve been using the eh, yes it’s moving coil, but can be used with a mm phono stage (47khom). It gets hardly anything but 5 star reviews, which tells me it must be pretty versatile. 

Never heard you table/arm, just a thumbs up for Audio Technica Microline’s, I have prior model 440ML. AT’s 540ml price is shown $370. Amazon $250.

https://www.amazon.com/Audio-Technica-VM540ML-MicroLine-Turntable-Cartridge/dp/B01MEI1RPC

People say specs are not a reason to choose, but imaging of a group of musicians, jazz players especially for me, is important because it is so enjoyable, and hearing the skills of individual players reveals their magic. Also appreciating the work of great engineers. The stiffness of the cantilever material is a determinant.

IOW, while checking reviews of sound qualities ... keep an eye on the specs.

Recently, I compared sound and especially imaging from 4 cartridges, using very familiar well engineered evaluation tracks. 3 arm deck allows instant comparisons. Center is phantom created by matching l/r. I can definitely hear the tighter center imaging, and how wider separation ’lays’ the instruments out more distinctly across the stage, that helped by the tighter center as well.

CS 25db; CB 1.5db Shure V15VxMR with new SAS stylus on boron from Jico

CS 30db; CB .75db AT440ML OEM Microline on aluminum

CS 30db; CB .5db AT33PTG/2 Microline on boron (MC, my first, and now favorite).

CS 25db; CS 2db: Shure 97xe elliptical on aluminum

I like the brush feature of the Shures, but both Audio Technicas produced very enjoyable sound quality while producing improved imaging.

I'm suppose wide frequency response, especially lows and their subsequent overtones is involved in the results:

AT33PTG/2 is 15-50,000hz
Shure 97xe is 20-22,000hz 

Specs: directly comparable to each other???, I just refer to what they publish.

I'll second the hana eh recommendation. I use the el version and it is lovely. 

If trying high output MC, like Hana EL, directly into MM Phono, it's still only 2mv. 

IF you have any hum when you turn your phono/preamp/amp volume up, I suggest sticking with MM as OP wants to do.

Thank you all for your input, I really appreciate it!
My reasons for potentially choosing one of these four cartridges are price and accessibility.

My system is modest, so regarding price I’d prefer to stay under $500. $350-$450 would be the sweet spot. I’ve heard the Ortofon 2M Blue and Nagaoka MP-110 on other turntables, of the two I liked the Nagaoka better.

But I like the way the Ortofon mounts better than the Nagaoka carts, with the top screws. So my hope is to learn from someone with a Rega 330 tone arm who has actually experienced these carts. Maybe the Bronze would sound great on it, or maybe the Nagaoka is a better choice? I have no experience with the AT or Sumiko carts.

I have not had hum issues thankfully, I use the phono stage built into my Marantz PM KI Ruby integrated, and it seems solid. As a relative newcomer to this hobby, it is quite helpful to learn from all your experiences-thank you for your generosity to share what you have learned!