which turntable or how to convert to balanced phono setup?

Most tables have RCA out only. It is unusual still to have a balanced out. I have never tried modifying a table for balanced. But I am sure some people here have done it. I'll be interested in hearing what they have to say about the sound quality as a result. 

If your are new to vinyl, I'm not sure this is where I would start. The key is high quality phono stage, table, arm and cartridge. This would be a side project I would try after being well into the pursuit. 

Most turntables/pickup arms provide inherently balanced outputs although - strictly speaking - they’re really floating. That is, they have a separate + and - for each channel, and a ground that is not connected to either. (That’s the purpose of the separate ground wire.) You need only to connect those outputs to the inputs of a balanced phono preamp to enjoy the benefits of a balanced phono stage. Those benefits include resistance to RFI/EMI and potentially greater gain (or better S/N), depending on the design of the phono stage. To be clear, you won’t get those benefits if you don’t also run your phono stage’s balanced outputs into a balanced line stage.

The type of connector is really secondary - there are balanced phono stages that accept only RCA connectors on the inputs. (ARC, for example.) In your case you can use either the RCA or XLR connectors on the Teac PE 505’s inputs and get the same result.

The Wiring Configuration from Cartridge through to the Connections used for the Tonearm Wires will supply the Balanced Configuration for the Cartridge, to then be attached to the Phonostage.

The Turntable itself, does not contribute to a Balanced Set Up. Additionally neither Stereo or Mono are coming from the Turntable, these are embedded into the Hard Medium being the Vinyl LP.

For the Noob, think of the Vinyl Replay Source as a Trilogy > TT > TA > Cartridge.

There will be those who give the Trilogy an order of Priorities to be considered and worked towards.  

Just buy the TT you really want. Don't base the decision on the cable connection. If you use the XLR output of the TEAC, it will give you more gain (4V as opposed to 2V from RCA). That's about it. You might notice it, you might not.

congrats audiocanada w/ pe505! 

phasemation explained well how to connect rca to balanced phono-amp: https://www.phasemation.com/product/cc-1200r.html  https://www.phasemation.com/product/t-550.html