Definitely use booth out. Being able to turn the monitors down when you don’t need them and control their volume separately from the master output is a good thing!
Booth out on the SZ is balanced Jack (TRS) I think, so the cables you are getting will work. Then again, you probably have XLR/XLR cables that you normally use already. If you are not using them to hook up your controller to the venue system, then it’s cheaper to get a couple of TSR to XLR male adapters and use your existing cables.
I am, BTW, with Caleb. Your HKs DO seem to have combo’s. You can tell by looking at the center of the input XLR. On regular XLRs there are only the three small pin holes, on combo’s there’s like a bigger (1/4″ duh!) hole in the middle that kinda connects the three smaller pin holes together. The middle hole will exactly hold a 1/4″ TSR connector.