Hi Rohrgatz,
You should still be able to find a mattress that fits your criteria for under $400 (you can see an example here) although of course in your budget range you won’t find the highest quality materials or components (it will range from junk to reasonable depending on where you go).
If you let me know your city or zip code I’d be happy to let you know about any of the better options or possibilities I’m aware of iin your area where you may be able to find something similar.
I would avoid the major brands (see the guidelines here and the information in the mattress shopping tutorial here).
A box spring (with springs inside it that actually flex) will change the feel of a mattress and it will feel softer compared to having the same mattress on a non flexing surface such as the floor.
Phoenix