Just buy a whole darn mattress, such as this one (listed at $260 for a queen). Don’t bother with a pad. I did this a few years ago and it’s worked great.
It comes in a tube. You open up the packaging and FOOOMP - a whole freaking mattress expands out of the thing. You leave it outside in the sun a couple days to outgas all the fumes that were keeping the plastic pliable so it can expand like this.
The first time I lay down on it…ah. You can instantly tell it’s the good stuff. It’s totally silent, you kind of sink into the foam leaving an inprint temporarily, you can sleep in a lot more positions and it’s still comfortable, etc etc. I just left the old boxspring under it, though you can also get a platform bed (just a sheet of wood and drawers under it) and slap the memory foam mattress right on top. You do not need anything underneath it, it works perfectly alone.
I could see a memory foam pad on top of a spring mattress. I would NOT want just a memory foam mattress on box springs. When I was driving, they gave me just a memory foam mattress for the sleeper. It wasn’t all that good and I was very happy to swap it out for a new spring mattress.