I am right handed and right eyed. The camera is big enough I don't think that should be a problem, but I haven't had to use it that way so I don't really know. The Super Press 23 is a great camera. You can do a search on RFF and find some useful comments on both the Universal and the 23.
Holding the camera with the left hand and focusing with the right wasn't really a problem with me, just something to learn if I wanted to use it. I felt better about it since the handle had a shutter release, and the roll film backs other than the multiformat, had a 35mm-like crank to advance the film. I have seen other MF RF and SLR, and felt I would be less comfortable with them over my 23. But that is just my preference.
I sure liked the big negatives, 6x7 in my case, since I don't think I even knew I had a choice when I bought it. I convinced myself that 6x7 was what I preferred, and held that opinion until I got a 6x9 Zeiss folder. Now I believe that 6x9 has a place in photography, but defer to the Zeiss, or 9x12 backs in 6x9, or cut film (cut down) with the 23. I don't do enough 6x9 to buy another back and anyway I have six 6x7 backs.
I found 100mm and later the 65mm a good selection, especially since that was all I could afford at the time. I later got the 150mm, 50mm (incredible), and the 250mm RF coupled lens. That one is nice enough, but requires a caisson with a crew of two men and a boy to carry around. 😀
It is absolutely a system camera, and not so heavy as some might think (assuming your back is in good health). For some time my back wasn't, which got me into folders. I haven't really gotten back into the 23 as folders, especially 9x12 have become something of a fascination for me. I need to get back into using it for the nice selection of lenses. I hope you enjoy yours.