My suggestion would be to try the equipment forum instead. I'm very pleased with my House of Staunton Grandmaster set but that was significantly over your budget of 100$. At 100$ (and even at what I paid) the sets are kind of hit and miss and you can get good or bad copies.
There are multiple ways you can save money. You can go with smaller King Size. You can go with some of the less well known brands.
Anyway, head over to the equipment forum and ask there.
I'm kinda new to chess and I'm wondering where I can get a good quality chess set that won't break the bank, preferably something I can easily transport and made of wood. Any suggestions?