The stock cooler will do the job.
It might noisy when it spins up under load.
The arctic 11 will be no better, it has a small 92mm fan. H45 will not cool any better either.
The only reason for an aftermarket cooler is for quiet operation.
For $35, you can buy a scythe kotetsu, one of the best and quietest coolers.
FWIW,
----------------how to mount the stock Intel cooler--------------
The stock Intel cooler can be tricky to install.
A poor installation will result in higher cpu temperatures.
If properly mounted, you should expect temperatures at idle to be 10-15c. over ambient.
To mount the Intel stock cooler properly, place the motherboard on top of the foam or cardboard backing that was packed with the motherboard.
The stock...