To answer your questions:
Upgrading to 3.9 does not require an LCD and will not benefit specifically from it, you'll get exactly the same screen-modes as, say, 3.1.
An accelerator will improve your experience with screen-modes with higher color count.
You can also get a graphics card (if one can be installed in your Amiga) which will give you more options regarding resolutions and color-depth.
As for CRT vs LCD, from my experience, it all depends on what you do with your Amiga.
Yes, higher resolution & more colors makes for a pretty Workbench, but has no effect on games, which will look better on a good CRT.
In MY opinion, there isn't an LCD on the planet that can match a high-quality CRT (like a Sony PVM/BVM) with 15Khz content that was designed with CRT in mind.
At least, I haven't seen one, at any price.
Hi
If I am going to install Amiga OS 3.9 should I attempt to update my monitor to a LCD rather than using my CRT, I understand I wouldnt get a any improvement on the resolution.
Would I see a difference with an accelerator and OS 3.9?
Thanks