Get this or something like it for ease of use. Put in coffee grounds and water. Leave in the fridge for a day or so and shake a couple times.
For cheap coffee that you can find anywhere, Italian Roast comes our very smooth and chocolaty when cold brewed, which is plenty pleasant to drink black.
A French press is my preferred method for hot coffee as well.
I really want to get one, but it just doesn't brew enough for me. I brew 64oz every few days, so the size wouldn't cut it. I've messaged them multiple times suggesting a bigger one, who knows if they'll follow through.
Edit: For the record, here is one of my favorite devices for cold brew. Cheap, and brews 64oz easily!