I leave my cream on the counter to get to room temp, it seems to turn to butter easier that way.
If I am doing a cultured butter I will add the culture about 8-12 hours before I make the butter.
I use a Kitchen Aid mixer to do small batches (1 quart or so) and have a 2 gallon electric mixer that works well when I have enough cream, and a commercial butter mixer that I have never used. Some day.
To get the whey out of the butter, I use a potato masher and mash the butter in a bowl, add salt, mash, pour off whey as it comes, mash more, pour off more whey, then pack it into either a butter mold or a bowl.
I also rinse with cold water or ice water as I am doing the mashing part.
The Amish near me make the butter in butter balls, each is about 1/2 pound. They just mush it together and squeeze the whey out.
I will use the whey to make soup or stock. I use it in place of water. Adds flavor it seems. Other people I know will use it to boil pasta. And of course the animals love to drink it!