Got plenty of experience.... as I work for a company that hires them
As said, they can take off like a scolded cat. But press down on the handle as you start, then slowly move forward as you lower it and away you go, when you get the other end, lift up and turn round and start again.
As for taking off 3mm, no problem, just go across the wood to level it out and then 'with the grain so to speak' and it will will look lovely
. You can get a wide range of grades of paper (I do: 24grit, 40, 60, 80, 100 & 120). But would not recommend using the 24 on your floor!
What ever you do, don't try to rush the sanding, take it carefully and it'll look brilliant.
Most floor sanders don't get right to the edge (but you can get an edge sander as well
), or you can use a detail sander if you have one.