The "Dot Pitch" isn't the best and it also can't do very large resolutions (does 640 x 480 & 800 x 600 well and maybe 1024 x 768), but depending on what you want to use your A4000 for, I like my Toshiba "TIMM" 20" CRT monitor for most stuff. It is huge and weighs a ton, so you don't want to be moving it around much, but if you have a NewTek Video Toaster/Flyer, or Macro Systems V-Lab Motion, or GVP IV-24, video effects boards, then having a CRT that also does Composite Video input, is a plus. It beats working on the small 13" screen of a 1084S monitor.
At one time I had 3 Toshiba "TIMM" monitors, but sold one of them a couple of years ago, so now only have 2 of them in my collection. I don't know how hard they are to find these days, or how many were manufactured, but if you want to stick with a CRT monitor for your A4000, I think the TIMM is one of the better choices (subjective opinion of course).
Edit: Odd that the TIMM is not listed on the Monitor list at the Big Book of Amiga Hardware.