Cutting your own pine boards to replace the particleboard shelves and side panels in your Billy bookcase is likely to give you ok-but-also-not-exactly-straight-and-parallel results without a lot of specialized tools and techniques.
I also don't think a hand plane will help you with warped boards much, and buying sizable not-warped wood is gonna likely add to your cost unless you get lucky at Home Depot. I've never had as much luck with the DIY fixes for that as others. I dunno what the hand version of a jointer is but I don't want to find out. ;)
You don't need a lot of power tools to do pretty cool stuff, but cabinetry is one of the tougher things to do precision-wise if you're unpracticed or don't have tools that make it easy to get repeatable results.
I make quite a lot of furniture from scrap or salvage - that's quite fun.