About several years ago, when I got interested in coffee, I picked up a device called the French press from the local target store for about twenty bucks. It was a basic Bodum unit with no bell and whistles, just the main glass carafee and around it is the black plastic housing and with the basic filtering top. I used for a long while and was extremely happy with it. However, I found that it is too big for my personal use ( I don't remember the capacity but it can make enough coffee to fill three mugs). I find that if I want to just make a mug worth of coffee, I would need to put only about 1/3 of the capacity of this French Press.
Then, I found a good deal on a very small bodum (which is three cup unit which is enough to fill a big mug); it is the Bodumn Chambord model which is their classic model. I was very happy with the build quality, and the good look of the unit. On top of that, it is the defacto way to make coffee; very transparent to the varietal characteristics of the coffee. Despite the silt that is alway at the bottom of the cup, I find that I'm not too bothered with this, I just had to learn to not take that last sip. Additionally, since I roast a lot of coffee at home, a lot of the coffee do not produce optimal result in espresso machine; however, most coffee taste fine in the French Press only after 12 hours rest.
For the French press that I have, I tend to prefer to use the finer grind, but courser than I would use for the aeropress; because due to the smaller volume the water teperature would drop quickly over long brewing time. I like to target for a brew time of less than three minutes.
I also like to preheat the french press before putting the ground coffee in for same reason. My favorite mug also get preheated as well, of course. Cleaning with the french press is ofcourse a huge disadvantage compare to Aeropress. I tend to not use dish washing liquid in my french press, I rinse it very well with hot tap water and plunge the plunger up and down several times to dislodge any remaining coffee bits. After about five brewings, then I would wash the french press very well with dish washing fluid as I find the excessive build up of coffee oil impart bad taste to the coffee.