So you buy a nice two shelf bookcase but it’s wobbly and you know it won’t hold much. I’ve recently gotten one and my solution was to put L-brackets on it. After installing about 8 of these brackets at the cojoining parts of the shelving, it is now completely stable and ready for use.
You could look at inflatable roll mats for camping, we’ve got a double one which is about 10cm thick and it’s nearly as comfy as our actual bed. It wasn’t cheap, I think around £200, but definitely a lot cheaper than our mattress.
I’d avoid air beds, I don’t find them comfy at all.
The other thing you could do is look for a mattress on 0% interest credit. We brought our Simba mattress on credit over a year or so for £20-30 per month.