I laid on top, partly because I could not easily cut the bricks but also for speed, and I decided out of all the bricks that might need to be replaced the ones right under the oven wall where least likely... this might be totally false tho given they get far more weight and you push the fire onto them during cooking but I am not sure I have seen anyone actually replace any bricks so far.
I think it depends on how you want the first ring, some folks have it outside the floor but do them standing on end to make a little extra height before the dome starts to bend for more working room and I can see some good logic there.
I wonder how everyone went as a %, I am going to guess its probably close to 50:50.
I also think it's 50/50. Myself I find it easiest to build my first ring then lay the hearth inside of that. For those awkward cuts around the edge I soak the bricks and cut them with a 9" angle grinder with a diamond blade. I cut what I can with a hammer and bolster........they don't have to be perfect as when you peer in afterwards.....they always look perfect, regardless if they're not.
I cut my floor bricks, then put a 1cm spacer around them before putting up the soldier course. This was done with newspaper, which burnt off during the first burn. The gap then fills with ash, which is compressible.
The idea being that as the floor expands from the heat, it shouldn't "push out" the soldier course, which would cause cracks.
Keep in mind that many ovens in Italy have a terracotta/clay tile floor over the fire-bricks. So if your bricks crack particularly badly, and you aren't able to replace them, you can always lay a second floor of suitable tiles over them (assuming you can convince someone to crawl into the oven and lay them for you )