I've spent some time choosing the most straight pieces from the lumber yard but they are still not perfect.
I was getting ready to to say be more selective then got to this sentence. So instead, be even more selective :-) A lesson I picked up somewhere very early on is if you must build decent stuff, especially furniture, from construction lumber you need to pick only the best stuff (leaving the rest for someone else who doesn't care as much) or expect to do A LOT of milling later.
Construction lumber is just that, it's made for construction, where many sins that are unforgivable in furniture work are acceptable. (It's still not as good as it should be frankly, but it is what it is.)
Anyway this also indicates that you didn't further process the wood before using it, which compounded the first error.
So, just a quick primer on buying SPF for anything other than rough carpentry:
- Be hyper-selective what you get, because it's sure not likely to get any better once it gets into your home/workshop. 1
- Do not expect to use the wood soon after you get it home. 2
- Still expect to have to do at least some milling to get acceptable parts!
3
I kind of expected that and initially thought that I could mitigate that by installing adjustable legs at the bottom but now I realize that I won't be able to fit the top plywood piece (the seating).
I wouldn't bother using adjustable feet here, you could simply shim the raised corners. Shimming is a perfectly acceptable building practice even in fine carpentry to get square items to fit in non-square locations, or the opposite :-) If for any reason you must have something adjustable you can install lag screws or bolts as feet, for a very large range of adjustability at almost no cost.
Spend all your adjustment time getting just the top flat and level because this is really the only critical surface on your carcass. Unless the distortion is very bad the top should easily be brought to level with some hand planing.
1 Accept no twist (literally none), minimal bow (a lot of this can be taken out when cutting down to size) and zero cupping. Discount pieces with too many or too large knots while you're at it. Depending on where you live and how many big-box stores or wood suppliers you have within acceptable driving distance this might mean visiting more than one of them, or ALL of them, to find the wood for a single project. Or, visiting the same one or two multiple times over a period of weeks in order to build up stock of the best stuff on offer.
2 Dimensional lumber should be acclimated at home before use. Don't think days, think weeks. You want to wait at least a few weeks and ideally longer; remember this is the wait time after the last piece gets home, not the first one. Wait more than a month if you can....... it still won't be as dry as it should be, but it'll be better. Even though you aren't starting with green material this is still drying wood and the lumber should be treated accordingly — sticker and stack it, with heavy weight on top.
3 A slightly bowed 8' 2x4 is acceptable because it will yield 2-3 project pieces which are very much less bowed than the starting board. But don't forget that no furniture pieces should have any bow in them at all, so before use in the finished project what little remains should be milled out, typically with a jointer and thickness planer or by planing (with a hand plane or with a power planer). It's not ideal but if you had to you could also do this using a belt sander fitted with a very coarse belt; you want to use well under 80 grit here if you can get it.