Hi. I was in the same boat a while back, feeling the springs on my old mattress. I ended up getting a thick mattress pad, and it made a huge difference. It added extra cushioning and made the bed way more comfortable.
As for finding a new mattress, I’d recommend checking out memory foam mattresses. They have that “sinking in” feeling you mentioned, and they’re great for back support. Brands like [edited by Mod] are pretty popular for their comfort and quality.