I have never shot a machine gun, but there are a few that I would love to shoot. (I'll leave out the .50 BMGs since you probably wouldn't want to pay that much for ammo.
Thompson M1928A1 submachine gun-----(600–1500+ rpm)(45 ACP)
M249 light machine gun (SAW)-----(750-1000 rpm)(5.56x45mm NATO)
M16/M4-----(650-950 rpm)(5.56x45mm NATO)
M1919 Browning machine gun-----(400-500 rpm)(30-06)
H&K MP5 submachine gun-----(800 rpm)(9mm parabellum, but some come in 10mm or .40 S&W)
IIRC, there is also a full auto Ruger 10/22. That would be the cheapest to shoot.
Just a few I'd like to shoot.