I know you've probably already made up your mind but I'll offer some advice based on my own experience.
I have been using two A1200s with the same LCD TV/Monitors for some time now. One of the A1200s has an Indivision and runs Workbench in 1024x768. It is crystal clear and never flickers. On the other A1200, it's running Workbench in 680x536 through a cheap RGB-S-Video adapter from amigamaniac.com in PAL with the maximum overscan that will fit on the screen. The pixels aren't as sharp as the Indivision, but the image is clear and solid, and never flickers thanks to the LCD TV's built-in flicker fixer. If I really need to, I can switch the resolution to 1360x536 and put the TV in 16:9 mode, which gives me heaps of room for those wide websites, but I still prefer the regular resolution for most things. I never have a problem fitting any Amiga software on screen, it's really only those large websites that you need to scroll around a bit. Even the Amiga.org proxy resizes the website to fit in PAL/NTSC resolutions so it's not a big problem not having 800x600 or above modes.
I wouldn't worry about a big, bulky multisync monitor if I were you, since LCD TVs do a pretty good job as monitors for Workbench as well as games, and of course you can watch TV on them too. Just make sure you get a LCD TV with either Scart or S-Video, and then get the appropriate connector for the Amiga to hook up to it. If you can take your Amiga into the shop and test it out before buying it may help make the best choice, but make sure you keep the receipt in case you need to return it for another more compatible model. I have noticed some LCD TVs handle the Amiga better than others, some won't accept non-interlaced modes (no low-res games will work) and others have this strange intermittent jump every five to ten seconds, which may be barely noticeable to some people but could drive others crazy.