No, the time of day doesn't matter at all.
The amount of time you have to spend depends on your goals. If you want to win an Age, you'll have to put in a lot of hours.
Especially in war situations it's important to be online, to see what your enemy is doing and to be able to act and react.
If you're offline for long periods of time (8h and above) every day, you propably should play on S2, because then you won't miss too many Turns.
If you're able to be online for a couple of minutes anytime you want, you should try S3.
I suggest you try to play on S1, it used to be our one and only server, so its speed should be suitable for most players. If it's to fast for you, move over to Server2, if it's to slow, join the game on S3