You're probably going to have a hard time finding one for less than $100, but I agree with others that a table saw is the tool you're looking for. It'll be efficient and accurate, and it's also the tool designed for what you're trying to do, so it'll be safer as well. Trying to rip narrow boards with a jigsaw or circular saw could get dangerous. And it'll be slow.
If you don't need it very often and aren't ripping huge things like sheets of plywood, I don't think you need to get an expensive one though. If you are only doing small rips, then a lighter table saw
should be fine. If you have heavy pieces like plywood then you either want a heavier saw or you'll want to bolt your saw to the floor so it doesn't move while you maneuver the wood. I'm pretty sure they even make mini versions now specifically for people who don't need to cut large boards.
You may be able to find a used one for cheaper. As long as it isn't abused, a table saw will last for decades. Lots of folks have an initial saw and then upgrade at some point, so used saws aren't too hard to come by. You may need to replace the blade - look
online or check Harbor Freight for cheaper blades ($10-$20). You don't need an expensive one unless you're doing fine woodworking. Research blades and get the right one for your job. It should say on the package what the blade is designed for.