My Artic Mini has a vertical monitor.
I totally recommend vertical monitors for either your second machine, or for a low cost first machine.
The reason I say it is low cost is because a HUGE percentage of the classics are vertical (and most were alternating play instead of simultaneous play), which means you can get by with a $40-$50 surplus computer, a single joystick, and 2 or 3 buttons. The low number of inputs needed means you can do a cheap and easy joystick hack rather than shelling out the cash for an I-Pac.
My Artic Mini hardly cost a thing to build at all. (Free cabinet, $75 21" kiosk monitor, traded about $30 worth of stuff for the computer, joystick I hacked was $3, overlay was $2, and then $20 worth of new controls for a grand total of about $130).