Early morning shows (10am onwards) tend to be for little kids (eg puppet shows).
The main shows start from 11am, and are definitely thriving in the afternoon. It goes well into the evening/night.
What you do most of depends on what you like. Without seeing the programme, you can't really tell.
As someone posted upthread, try to go to a 'pick of the fringe' event (Mervin and others). These tend to run around lunchtime in the main areas (Pleasance, George Square), and will give you a taste of about six shows.
When you buy tickets, try to cluster them in one area, so that you are not dashing across town, eg Pleasance one day, George Square the next.
Most shows are around 60 - 75 minutes, and you really need a gap of about an hour between shows (to get some lovely Edinburgh Gin and snacks, and then to join the queue for the next show).
The atmosphere in the Pleasance and George Square is really buzzing. I haven't done George Street, but it looks the same.
Don't underestimate how exhausting it can be, especially as Edinburgh city centre is quite hilly.