You need change nothing.
But... I have a few thoughts:
I3-6100@3.7 is a very good processor and appropriate for a GTX1060.
There are other options;
For the same price, the newer gen i3-7100@3.9
or, G4620@3.7 for less.
The caveat is that a H110 motherboard which is cheap will require a current bios to run kaby lake.
Motherboards manufactured after about 11/2016 will have the enabling bios.
If the bios is old, you would need to borrow a 6th gen cpu to do the flash, or take it to a local shop to get it done.
To be safe, a B250 motherboard would be fine.
Buy a 2 x4gb ram kit so you can operate in faster dual channel operation.
Do not count on later adding a 8gb stick, it is not guaranteed to run.
If you eventually want 16gb, it is better to buy a 2 x 8gb kit up front.
Seasonic S12II 620 is outstanding.
I3 will come with a adequate stock cooler.
The only reason for an aftermarket cooler would be to get a 120mm fan which will be quieter under load.
Scythe kotetsu, cryorig H7, or cm hyper212 are all good and inexpensive.
All, including the stock cooler come with paste.
You said nothing about a drive.
I will never again build without a ssd for the "C" drive. It makes everything you do much quicker.
120gb is minimum, it will hold the os and a handful of games.
But, many things default to the "C" drive.
When a SSD nears full, it will lose performance and endurance.
240gb is the recommended minimum.
If you can go 240gb, or 500gb you may never need a hard drive.
You can defer on the hard drive unless you need to store large files such as video's.
It is easy to add a hard drive later.
Samsung EVO is a good choice for performance and reliability.