I started reading about Bitcoin a few weeks ago. Reading most the information and watching videos on the web, I though I understood about the mining process. However, I was shocked when I realized than all the 2^32 combinations of possible values of Nonce can be found is less than 1sec with the current mining hardware. I was even more shocked when I saw the explanation that the mining process also includes the selection of each transaction will be processed. Thus, mining process is much more "try to find the transactions" that will provide the solutions than really try to find the correct Nonce. When the solution is found, then does the miner publish the list of all transactions he selected, the Merkel Root and the Nonce. If the miner's solution is correct, he receives the block reward (currently is 12.5BTC) plus all the transactions fees included in the publish list (not all initial transactions).
At the same time, the concept of "Priority transactions" (https://en.bitcoin.it/wiki/Transaction_fees) no longer applies , since the miners choose the transactions to be processed.
Is my understanding correct?