I've got to make a presentation but I don't know the ratio of the screen it will be viewed on. It will also have to be available in printable version (A4). What slide ratio is more appropriate given these constraints? Any suggestions?
I'd use A4 landscape to match your printed output.
Any software likely to be used for on-screen display (Acrobat, Powerpoint, Impress, a video player) should be able to scale this proportionally to fit the display device in full-screen mode, leaving black bars at top and bottom.
A4, at 1.414 ratio, is a bit wider than traditional 1.33 screens, so will be a reasonable compromise for widescreens (usually 1.6 or 1.78)
1024x768 is to my knowledge the most common "safe" resolution. Most beamers support it.
If you use powerpoint then your layout can get compromised if the resolution is very different or if the font is missing. So maybe also look into font-embedding or consider Acrobat as a format.