As to the proper amount of slack in the chain, new or otherwise, is you should only be able to left the chain from the center of the top bar, so that you can only see the drive tooth of one (1) of the links.
Now with a new chain, the trick is to check the slack after the first tank of gas has been consumed, as new chains tend to "relax/stretch" after being put into service.
But with that being said, I always check the chain at each fueling and filling of the bar lube tank too. Better to be safe and get the maximum performance from your chainsaw, and there is no better way than to keep everything in proper working order.
A good rule of thumb is to:
- check and readjust/tighten the bar/chain after the fuel tank runs out of gas/oil mix. (wait for the chain/bar to cool before grabbing it with your bare hands!)
- Refill the bar/chain oil
- Refuel the chainsaw with the proper gas/oil mix, (typically 40:1)
- I always add fuel stabilizer to my fuel tank after I'm done using it for the day (who knows when you'll use it again!)
- Take a hand file and give the cutting chain a quick "touch up" sharpening before putting it away.
If you follow these steps, you'll always have a working chainsaw, ready and sharp enough to cut when you need it, without any surprizes, etc.
I hope you find this Very Helpful and best regards!