Hi Andy,
To be honest, if you mean resolution as in dpi (dots per inch) then that's fairly immaterial when it comes to posting images on the web. The reason for this is that the resolution of computer monitors is fairly standard and is governed by the number of pixels that fit across and down your computer screen. There's a table here:
Scanning Basics - Why 72 dpi? that lists the Apparent Resolution of different monitors sizes and screen resolutions. The measure of dots per inch only really comes into play when you are printing the image.
The upshot of this is: there will be no visible difference on most computer monitors between a 72dpi file and a 300dpi file - it's just that the 300dpi file will be larger and will take longer to load in a web browser.
As far as image format for the web is concerned, the general rule of thumb is as follows:
JPG - used extensively for photos and other continuous tone images on the web. Uses lossy compression by trying to equalize eight by eight pixel blocks; the quality can vary greatly depending on the compression settings.
GIF - supports animated images and transparency. Supports only 256 colors per frame, so requires lossy quantization for full-color photos (dithering); using multiple frames can improve color precision. Uses lossless LZW compression.
PNG - uses lossless compression, offering bit depths from 1 to 48. It was mainly designed to replace the use of GIF on the web. Supports transparency, although there are issues with Internet Explorer.
In a nutshell: use JPG for photographs or artwork with fine colour gradients, use GIF for simpler images, animations etc.
Hope this helps.