Cartridge (other than Rega) with Rega RP10

Ladok, sorry especially one responding earlier. But yes, I consider the Lyra as a house sound. I find they have a delicate revealing sound with over analyzing. Top to bottom I find them to deliver what is ever in the groove. To a point that I have experimented with adjustments and find that extraction increases as if the cartridge can read it, if the tonearm settings and cartridge alignment are correct. That said, I am sure this is with any cartridge, the full potential of a good cartridge is dependent on set up. Like the best tire can’t fully perform with bad alignment and suspension. 
As far as the Lyra House Sound, you need to experience it to know if you will love it. Is there a Rega dealer in your area that sells Lyra. See if he is willing to set one up for you. Regardless of which cartridge he uses, you should get a feel for the sound Lyra brings to the table.

Lyra is very expensive cartridge, it depends how far you can go ... 

Dynavector KARAT 17D2 or next models with short Diamond Cantilever could be a good choice for less money. 

I have a Sumiko Songbird that I broke right away and have rebuilt now by Andy from Needle clinic with Saphire micro Ridge. I’m using a orthofon 2m for now. How would you guys rate my songbird over the Lyra?

Where I am the 17Dx and Rega Apheta 3 are the same price and the Delos is cheaper than both. The 17D3 used to undercut the Delos but the change to the brass bodied Dx came with a hefty price increase.The Rega will have a good chance of correct VTA on a Rega deck, you’ll have to shim the others if they need adjustment.

Dynavector with short Diamond cantilever is great and this cantilever is very well protected, the other two cartridges with long cantilever in front of the cartridge can be smashed easily and it will be a tragedy. 

17DX
17D2 mkII 
Delos 
Apheta 3