XLR connectors

I have 4 different brands of balanced cables, all with different looking connectors. I can't hear a difference in any of them.

Along with the good advice by those who have posted a comment  here, Chris at VH Audio will be very helpful for your XLR needs.

I recommend reading up on the Audioquest line of connecting cables.  They do a lot of R&D on the type of materials for the underlying metal and in the platting process.  They also do a lot of R&D on insulation type, grounding materials, and noise dissipation.  It's the noise dissipation that will provide the most sonic improvement for your system.  Audioquest makes a number of models that are not terribly expensive.  Of course, they offer a number of models that also approach stratosphere price points.  I have been using their line of products for more than 30 years, since the company was very young, and have always found them to be superior in so many ways, especially sonically.  I have always bought new product but you can easily find them used, on eBay, for about 50% (plus or minus, depending on age or demand) less than the price of new.
Good luck.  No matter which you settle on, do enjoy the music.

AQ makes good cables. I used to have their Diamond usb cable which at the time was the best usb cable you can but, this was probably 5 or 6 years ago. The last time I listened to various AQ cables, I would start with the Colorado version and go up from their (these are no longer made but I think the new model might be the Earth or Wind). The cables below Colorado had too many flaws for my tastes

With longer runs for interconnects, XLR definitely is better.  With my 18" wiring, I hear no difference when I switch from one to the other.  The XLR will stay plugged in, but I sent and amp module back for repair, and it was good.  I had a bad XLR adapter (Different amp)  from guess who, Radio Shack.