First of all, the state of Amiga emulation is excellent. The best emulators run Amiga software almost as if it were on a real Amiga. You can even choose screen filters to make it look like you are using a 1084 monitor, and have the floppy drive sounds.
As far as Linux goes, you have a few choices. FS-UAE is available in the repositories, and works fairly well. I was successful in setting up a virtual A4000 and A1200 using it. It ran everything I threw at it, so I think your problems are based on some configuration issues.
However, in the end I choose to run Win-UAE (the Windows Amiga emulator) under Linux via WINE, and it actually ran better that FS-UAE running natively under Linux (smoother, faster). Win-UAE is really the gold standard of Amiga emulators. I realise that FS-UAE is based on WinUAE, but it doesn't seem to run as fast or have as many user configurable features (at least in my experience, and the author admits this too I think).
If I were you, I'd just buy Cloanto's Amiga forever. It gives you lisence to the ROMs and a copy of Amiga OS3.1 as disc images. Amiga Forever is mostly Windows based, BUT, I it can be used with Linux in some way too (I have not explored this entirely, but certainly if you boot from the Amiga Forever CD it boots into a version of Linux running under the emulation. I would enquire with Cloanto about this. I'm not sure, but I think the Workbench ROMs from that package will also work with FS-UAE or Win-UAE, and you would have the legal lisence for them by purchasing the Amiga Forever disc/download pack.
It seems to me that Amiga forever would solve most of your problems.
I think your grey screen problems when playing games might be related to configuration issued in the emulator (i.e. not setting chip and FAST RAM correctly, or setting chipset OCS/ECS). Also, it's possible your trying to play an AGA version of a game on your emulated ECS Amiga 500, which of course will fail.
https://www.amigaforever.com/gnulinux/
