MM, MC, or MI cartridge

@rvpiano -- Don't toss that Virtuoso!  It is basically an AudioTechnica VM95 body.  You can easily replace the cantilever and stylus with any AT-VM95 stylus.  I've done it, as have many others.  I replaced the stock stylus with an AT-VMN95ML microline stylus.  Very nice improvement.  There are several guides on the internet on how to do this.

Thanks so much for the tip (no pun intended.)

I went from MM to MC and love it. Pro Ject X2. Sumiko Moonstone MM to Hana SL. 

All of the above advice is anecdotal (a story told by one person with no statistical validity). The best the op could do would be to read up on the 3 different transducers, and then listen for himself. It takes time and effort to figure out what suits you best.

@rvpiano FWIW I agree with @inna  - start by upgrading the RP3. However if you decide not to re-tip the virtuoso, the Hana ML is great for the money and a good place to start the MC journey.