Here are some hints.
Old computer monitors had screen format 4:3 (ratio 1.333). They could be 800x600 or 1024x768 (let's forget about 640x480 and 320x240). I think it's all in the past. I used a laptop with such screen for 5 years but since recently now I have a new one with significantly different possibilities

17'' and 19'' monitors have a surprisingly square format 5:4 (ratio 1.25). Typical resolution is 1280x1024.
Most modern formats are 'wide screens'. But they are different, too.
Most of the modern laptops and LCD monitors have 16:10 (i.e. 8:5) format (ratio 1.6). Typical resolutions are 1280x800, 1440x900, 1600x1000. This aspect ratio is the closest to the 'golden section' (1.618)
Some older wide screen laptops had LCD matrices with 15:9 (i.e. 5:3) format (ratio 1.667). I've seen a lot of laptops with such screens with 1280x768 resolution.
Some newer laptops and many newer LCD monitors have the same format as wide-screen TVs: 16:9 (ratio 1.778). Not very convenient for most computer tasks, but more and more monitors have that format. Typical resolutions could be 1280x720, 1366x768 (32'' LCD TV), 1600x900 (maybe, actually never seen such) and 1920x1080 (HDTV).
Usual office paper suitable for printing has format 297x210 [mm] (A4 format) with 1.414 ratio. Well, maybe you use other formats in America, like 'Letter' or 'Legal', but I know about them only from printer settings. Never seen a single sheet of any of such formats. We use only A4 or A3 here.
Traditional photo frame had 3:2 format (1.5 ratio).
I think I would prefer 1.6 aspect ratio. The size of a picture is a serious question, too. My current work is 1600x1000, but I can take 1920x1200, if necessary.
Take into account that large image would be downscaled automatically to lower resolution with the same aspect ratio, but smaller image wouldn't look as good on the monitor with greater resolution.
That's it and here is the poll