Depends on the game if your progress is saved online.
With steam you can copy across your main game folder to a new pc. On the new pc it will have to install and validate the games but overall it significantly reduces the amount to download and the total time taken. Google 'copy steam game folder' (I'm on my phone) and you should easily find instructions on doing this.
I did this a couple of years ago and it still takes time but much less than completely downloading each game. How long it will take is impossible to say. Will depend on the size of each game, your pc and internet connection.