If you can find a 4:3 CRT computer monitor that's would be the way I would go. A 20" computer monitor (which is pretty hard to find in my area) has a 19" tube, which is the same size as most of the classic games on a 60 in 1. I am currently bringing a stripped Dig Dug cabinet back to life and I went with a 19" CRT monitor because I cannot find a 20". 19" computer monitors have a 18" tube, so its 1" smaller than the original arcade monitor would have been. That said, I think its big enough. I am using a 60 in 1 and I think it looks great using the VGA out from the 60 in 1 to the CRT monitor. A CRT monitor has a sharper picture than a standard resolution arcade monitor, but it still has visible scan lines, and looks pretty darn good with the 60 in 1.
A word of caution if you plan to use an LCD. A 19" LCD is easy to find used, for $10 or under. I have a few that I use in horizontal builds. If you plan to go with a vertical monitor build, most LCDs have bad viewing angles, especially from the the bottom angle. Once you turn the LCD monitor on its side for a vertical build, the bad viewing angle from one side (the bottom angle when its horizontal) is very noticeable. There are a few LCDs with good viewing angles, they will generally be ones with IPS screens. In particular the Dell 2001FP and 2007FP have great viewing angles. The Dells are 20" 4:3 monitors and if you can live with an LCD, they are a great choice for a vertical build or for a cocktail table where viewing angles are very important. Lastly, for an LCD, I would suggest purchasing a hardware based scan line generator to hook up between the 60 in 1 and the LCD. They are around $25 and make the LCD display look a lot better with vintage games.
I attached a picture of my work in progress Dig Dug with the 19" CRT computer monitor mounted.