You're in a bit of a tight spot with this one. Remember, you're asking a lot for not much money. However, I think you're in luck. I've found this mobo: http://www.newegg.com/Product/Product.aspx?Item=N82E16813130897, Which has great reviews. It also currently only costs $56. It's got two slots for DDR4 ram, which will probably cost more than $30 if you go for a 2X4 configuration. However I did find this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820156108 . It costs $14.99 at the time of posting but is probably absolute garbage. I'd recomend instead going with this:
http://www.newegg.com/Product/Product.aspx?Item=N82E16820233982 . It's a 1X8 configuration so you'll have an extra slot on the Motherboard free if you ever want to upgrade and costs $30.99.
Don't forget to buy the rest of your build along with this (Cpu cooler, Case, PSU!)