You ALWAYS need a cpu cooler.
Most processors will come with an adequate stock cooler.
It will have paste pre applied for installation.
High end processors designed to be overclocked like the Intel K processors will omit the stock cooler since the buyers will want to select their own high end cooler.
What is your budget?
What will be the main use for this PC?
The key to a good build is the selection of parts.
Assembly is simple.