Aside from small specialty screens (Mainly POS/cash registers), I didn't really start seeing LCD monitors becoming mainstream in computer stores & general use until around 2005 or so. Yeah, LCD screens for desktop computers had existed LONG before then (I recall seeing one many times on the TV show "ER" way back in the 90s), but it really wasn't until 2005 or so that the quality had improved enough & the prices dropped to suitable levels for their adoption rate to really start ramping up.
For me personally, the first LCD flat panel I ever used on a desktop was a ViewSonic VA712b back in 2006. It was connected to the inventory management computer I used in the store I currently work at. In fact, the work computer I use is STILL using this monitor. This is a shared business computer though, so I really can't consider this computer and monitor as "mine" in my personal history.
At home, I cannot remember for certain whether the first LCD monitor I got was either for my father's or one of my own computers. In any case, the first LCD monitor entered our house around 2008 or so (Although getting cheaper, the cost was still a little too high for us until then). I got a new 21in LG monitor for my father's computer, but I don't remember the exact model. For my own computers, around 2008 or 2009 I got a used Dell 19in LCD to replace the HP CRT on my main desktop, and another used ViewSonic VA712b from work (It had died, but I figured out how to fix it) for my office computer.
As for 4:3 vs. widescreen...I actually have yet to personally buy, either new or used, a widescreen LCD desktop monitor. The four I currently have (The previously-mentioned Dell & LG monitors on my repair workbench, plus a couple other spares I have set aside which I can't remember the brands/models of) are all 4:3. Honestly, NONE of my desktop computers have ever been connected to a widescreen monitor of any kind*. It's not that I dislike widescreen, rather I had already switched to using laptops as my daily driver systems long before the mass transition to widescreen monitors happened, thus I've never had a need to buy a new(er) widescreen LCD for my own personal use.
*EDIT: I probably should clarify that my 2009 Mac Mini is connected to a 32in widescreen HDTV so I can use it as a low-end HTPC. I don't consider this a computer monitor proper though.