The typical monitor for the IIcx was the Apple 13in Trinitron Color Monitor, which gave 640X480 resolution (depending on the card). The switches on the VGA Adapter should be set for that - 640X480, with V-Sync, H-Sync and Composite on Green (or just plain Composite) all on. IF there is a setting for "LC" (as in Mac LC), then put it on that. The Viewsonic monitor should be great for it; there is a problem with older video cards working with LCD monitors, there's a thread on that here somewhere.

You should be able to turn on the IIcx without a video card and see if it chimes or chimes of death without the card. The Sound cords on the IIcx/ci are the same as on the Mac II series; depending if the scale goes up or down gives a hint as to which bank to look at. The notes can be found in the Dead Mac Scrolls Book. Other Death Chimes can mean other things - only about 5 or 6 are listed in DSM book. DSM can be found as a pdf somewhere online, or get a dead tree copy from Amazon.