It shouldn't be too hard to replace the old ceiling exhaust fan. You didn't say, but I'll be it has a chain hanging from the unit to turn it off and on, correct.
After you turn the power off to it, take off the ceiling cover (should be a couple of screws holding it on), then I use a recip saw and cut the nails holding it in to the ceiling joists, pull it down (this will reqire a bit of prying) and undue the wires, then take it out. You are probably correct in assuming that the unit just vents into the attic....most were installed that way many years ago. Your best bet is to run a 4" (or 6", depending on the vent duct size of your new unit) duct to the gable end and cut in a dryer type vent with a flapper valve. I would suggest this over a roof vent, as weather sealing a new protrusion through your roof may be a bit of a challange. The tricky part will be running wire down your kitchen wall for a wall mounted switch. You'll have to do some tricky drilling through the wall top plates to have an opening to snake the new wire through, and hopefully, you won't have any fire blocking in your wall. Your new fan may require you to enlarge your old opening. I like to install a 2X4 across the top of the new exhaust unit between the ceiling joists to help support it.