My boxspring is crumpled in pretty bad in one section and its causing back issues but i can't afford a new bed. i was told by the physical therapist to get plywood to stick between the mattress and box spring but i have zero clue what kind to buy. it needs to support the weight of the mattress but also me (425lbs) its a full size standard mattress and box spring on a regular metal frame where its open underneath.
Where is the damage in the box spring (middle/side edge/corner) and how much of it needs reinforcing? If the damage is in the mattress with seemingly good supports all around, just about any plywood half inch or thicker is going to work fine for this purpose. Since its going to be 100% non-visible, buy the cheap stuff. If its on the edge or corner, half inch would probably still be fine but I would probably buy something thicker just for added durability.
As an alternative, and since this is a DIY forum, I feel I must mention that box springs are pretty simple structures and it would likely be pretty easy to just repair your current one. They are mostly exactly what the name implies (a wooden box full of uncompressed springs covered with fabric). I would encourage you to take the back covering off (its held on by staples most likely so its easy to re-attach) and assess the real damage. Post pics of what you find here asking for advice if necessary but you are probably just looking at replacing a couple of broken 1x2. Take a piece of the broken ones to the lumber yard with you to make sure you get the same kind of wood (or something with similar strength) and replace the full length of the broken piece (don't try to replace just a section of it). If re-breaking is a concern, you can reinforce as necessary after the repair is completed or you could always add the plywood between the mattresses as well just for added assurance.
You'll probably be better off buying another box spring, cost and usability, around me I can pick up a full size box spring for ~$30 new while plywood is running $20-30 depending on thickness.
The box spring is supposed to be, well springy to some extent. If any of the box spring is still standing the mattress and the rest of the box spring will distribute the weight and you'll bow the plywood well before breaking it, any size.
If you're up for repairs and your box spring isn't clustered with metal like this one - though probably wrapped in some cheap skirting cloth - you can probably repair the broken beams with cheap furring strips and install more long running supports or block up the portions where weight actually impacts in the most, obviously the broken area but typically most people abuse the side they get in/out of the most. Talking about actual sleep patterns here, extracurricular activities might want repairs, blocks, and plywood ;-).
3/4" BC plywood should serve you well. It's fairly smooth and will have adequate strength in this application. The question becomes one of rigidity. If it proves too flexible, add another sheet of 1/2" or 3/4".
If you're able, cut it to roughly 2" less than the size of the box spring (so it's slightly recessed all the way around), round the corners, and run a router with a bullnose bit around the sheet from both sides. This will prevent wear over time from the mattress material rubbing on sharp edges.