A couple of years ago I had a similar creative urge, and ended up making 2 PVC bows. I wish I could have afforded the materials to make a better one (or had the time/skills to make a wooden one) but I had fun nonetheless. The costliest thing was the bowstring. xD
The first bow I made was simply to get my feet wet. It was a simple longbow made by sticking one PVC pipe inside a slightly larger one, and then stuffing a fiberglass rod in the middle. Once notches were made at either end, and a ledge to fire of of was added, the thing could be strung up and it was ready to go in just a few hours time. I tested the draw weight and it comes in at a hefty 40-50 pounds. Makes the thing hard to aim, that's for sure.
The second bow I made was where I got to stretch my artistic muscles a bit. I decided to model it after something along the lines of the nomad or horn bows in crpg. It is a smaller size with the recurve, and I believe it has the dimensions of some historical bows used on horseback. The fun part about that one was flattening it and then having to cut out various sections, smoothing it all out, bending it just right... long story short, it was a pain, haha. But I had fun. That bow is much weaker (only 25 pounds or so draw weight) but at least that is something reasonable that you can actually aim with. I'm not exactly gonna go hunting deer with my target-tipped arrows.
If you are on a budget I recommend trying to make a flattened PVC pipe bow. If the sky is the limit, go and buy all your fancy wood and metal crossbow parts,
.
Total cost of the longbow was probably 10 bucks, plus the additional 10 or so for the damn bowstring. Arrows of course cost a decent amount as well. You can literally use anything for a target, I started using garbage bags stuffed with grass clippings or hay. Then I upgraded to a cheap $5 foam target. The cav bow only cost about $5 for the raw materials (this one only require PVC pipe of one diameter... not two different sizes, and no fancy fiberglass rod of a specific size either), but if you don't have a heat gun, that can set you back $40 or so. You're gonna need one of those to
melt it so you can inhale all the lovely fumes soften the PVC.
If you are feeling more adventurous than I, you can also make you own homemade bowstring. But to do that you need to create your own rig for it, and track down a certain type of wax (everywhere seemed to suggest bee's wax, I think), and then rap the string around itself thousands of times. That is why I opted for the $10 per bowstring charge. ;)