If you're talking about the basswood sold for building models and stuff, sure you can use it. You "can" also use pine. If cheap and strong is your need, try oak. You can find oak lumber in the cut-off bin at Home Depot for next-to-nothing.
Basswood and poplar are both commonly used in less-expensive solid-body guitars. Largely because they're very easy to machine and not costly to begin with. The blanks are generally cut from three or more planks laminated side-by-side. Now, if you see a guitar neck made from poplar or basswood, just laugh and walk away.
Maple would be a better choice. Tougher and almost as easy to work with.
Absolutely, if you like a clear, almost white wood, go with maple. It's much harder than basswood, cheap, and resists warping and twisting very well. It needs a protective finish or stabilizing; I've sweated for years in dingy basements and smoky bars, all over "bare" maple necks treated heavily with tung oil, and all they did was develop a nice transparent amber patina. It can be dyed about any color you can dream up and is readily available in curly and birdseye figured grain. Tightly-figured maple can be a little tricky to work with, for instance birdseye's kind of feel like a knot under the chisel or knife. But neither figured nor clear maple will run out big chunks and splinters like softer woods can.
Somewhere in the back of my brain, lurks the idea for a cherry-burst flame maple handle on a nice clean drop-point, but that's another story...