I am using an LCD monitor on my Amiga 4000D. Its a Dell 2000FP 20" LCD. It's great and I don't even need a scan doubler (it has composite and s-video in meaning it can scan double stuff on it's own; although I was surprised it worked with the VGA port as well).
The only problem you will find with LCDs is that anything other than their native resolution (1600x1200 in my case) is a bit fuzzy. If you can find a resolution that scales perfectly (as in a direct multiple of the monitors native resolution) then you can still get a mostly crisp picture
This doesn't matter so much for games but does make a difference in a Workbench type environment. I would recommend the monitor to almost anybody and you can often get a good deal on one via eBay if you look.
Gabriel