The Jr3 is the only press I've ever had, and I used it this weekend. I have loaded .405 Win., 45-70, 40-70, 30-06, 25-06, 7x57, 30-30, and scads of pistol rounds on it, including .44Mag. I have formed 30-06 brass to 8mmx06 on it and load the 8mm-06. I do this with the RCBS liquid water based lube and their lube pad.
You will have no problem using it with any of the rounds you posted and many more. The only problems I have had with it are that the design for catching spent primers is awful, and with wear the arm tends to sink to the ram up position. I asked RCBS about this and they said that all their JR3's do the same thing and they haven't found a fix. I live with it.
I found it interesting that RCBS is still using their JR3's as well.