Technically, its called a Multi-effects Processor. But many shorten it to MFX.
For your budget and for firsthand, I'd recommend Zoom. Zooms have good tone and features. In fact, a Line 6 POD equivalent would cost twice as much as a Zoom.
I personally don't find Line 6 MFX that great, though their digital stompboxes are quite good. But yeah, they're very easy to use.
