Your best bet is already-made second hand furniture, both on environmental grounds and cost. I've been building my own furniture using basic DIY skills for quite a long time and it is rarely cheaper than Ikea-level new stuff. That's mostly because I can't bring myself to build with MDF or other cardboard-like materials, though.
Your first choice should always be free stuff that people are giving or throwing away, balanced against the cost of moving it to your place. If you can arrange to be around a university town at the end of an academic year you can generally furnish your apartment just from stuff that's being thrown out nearby. But failing that freecycle, craigslist and so on are good sources.
For building things, I find that construction sites and especially demolition sites are great places to look around. Many of them are paying to have waste removed so if you unofficially steal it from the skip they can avoid paying to have it removed without being responsible for what you do with it. If you ask they may have to say no just for liability reasons. I have obtained a lot of useful stuff from skips over the years, and on smaller sites they're often very accessible (ie, on the street). Note that legally it's still theft in most jurisdictions but if you're white and well-spoken you're unlikely to have a problem.
The health issues with second hand mattresses and soft furnishings mean that it's usually worthwhile either buying one off someone you know or just buying new. Since you seem to be at a university in the US midwest somewhere resistant bedbugs are possibly an issue, and if there's even a chance of those I'd buy a new mattress and bedding purely to avoid them. The same applies to fleas, unfortunately - if you see pet hair on a second hand couch it's worth avoiding it. At the very least take it home carefully, leave it outside until daylight then check it over when you can see what condition it's in. Getting rid of insecticide-resistant fleas or bedbugs is difficult, and often they will migrate into your clothes and apartment very quickly, meaning that once you touch it it's your problem.
Borer and termites in wooden furniture might also be a problem. It's worth buying a decent torch (easy these days) so you can investigate things on the side of the road before getting too excited about them.
That said, our apartment is largely furnished with stuff that is either second hand or home made. Most of the second hand stuff was free.
One tip is to make your own bed base, so you can make it thinner and higher than standard. That gives you a lot more storage space under it than a normal bed has. You mentioned welding in one answer, and if you can weld an angle iron frame with flooring ply plate sitting in it has worked really well for us for several years now. It has 2" angle with 1x2" square tube welded underneath for strength (so there are only 4 legs on a king size bed) and it's got about 500mm of clear space underneath. Flooring ply for the joining strip and strength - the bed is 2m wide and ply comes in 1.2m wide sheets, so there care two pieces. Also, the legs must be unboltable or you can't move it (trust me on this). We have a long drawer on wheels that runs up the middle of the bed because otherwise there's a dead space in the middle of the bed.