What is the lowest image size you make for a web site and with what extension,why we try to make the size so small and what are the programs you use?

If you are going to save vector work which has less colors always use PNG for bitmap colored images or complex graphics JPG is better i also use Fireworks , Best way is at time of Exporting image simple check PNG and JPG and save image in format which give less size without losing quality 

Regarding size just remember90's era is over now days size is not issue if you ask me i suggest you to use1 image sprites of100 or200 KB instead of loading201KB or less small files 

As many connections your web page generate its slow down loading time so try to minimize number of connections 

the best images size depending  on the website design, but the lowest size always i looking behind for each image to be less than1k and the best way is spirit images, with png extention and indexed type, why we make it smaller size, sure to get best performance for our websites, to be honest, i like adobe firework cause its give me best size with good quality.