Get a foam mattress off Amazon, we got a queen size for $300 a couple years ago and it’s beat out all other mattresses we’ve used to date. Do not go to a mattress store and spend 4x the price, it’s not worth it.
Here’s one that’s very similar to what we bought. Sleep Innovations Marley Cooling Gel Memory Foam Mattress, 10 Inches, Queen https://www.amazon.com/dp/B00H2RSA88/ref=cm_sw_r_cp_api_glt_i_8AX4PP6YPGHGX5NHF5E2?_encoding=UTF8&psc=1
If your budget is that tight, you could do something like this. It's mafe.by the same parent company that makes the Novaform for costco, FXI.
Personally, I think the Sleep Innovations mattress on Amazon is pretty nice. I bought mine in the queen size for $246. It's a 10 inch foam mattress that's pretty plush. It is more on the soft side so if you like firm mattresses, I don't think it will work for you.
Also, it does have a kind of chemical like smell (think new-paint-on-the-wall type of smell) when you take it out of the box, but it goes away after a few days.
Here's a link.
https://www.ikea.com/us/en/p/haugesund-spring-mattress-medium-firm-dark-beige-80307416/
You could add a topper to this and it would probably work fine.
https://www.amazon.com/dp/B00H2RSA88/ref=cm_sw_r_cp_apa_glt_fabc_RD7DSWCGX40TTZRWV2CK?psc=1
Same here. There's a 12" version of this for $349, but it's in possible to tell if it would be soft enough to not need a topper. It would be softer than the 10" though.