its a fairly average deal apparently, i picked up my JS550 (complete running jet ski) for $350 [from el segundo] and recently a spare JS550 motor for $80 [in sherman oaks]. mine didnt come with a choke so i'll transfer that and play with the spare motor. they apparently last a LONG time, longer than the ski itself. i think they're 6v stock but mine has a 12v battery cuz IIRC the guy converted it.
if you get the motor, buy a manual, they show you everything and mine was about $30. to give you an idea, the JS550 i have is 2 years older than me (its a 1983) and has 135 compression on both cyl's so its still perfectly running.
we are in so cal, you may find it just easier to buy a bike motor than mess with cooling, if you bust your pipes or spring a leak, your 'cheap' motor will fry and will become a $250 paperweight (calculate in the parts, radiator, pipes/hoses, etc..) i think they use something on the driveline to pump water in but i cant say for sure right now. if that is the case, you would need a pump.
one last thing regarding kawasaki jet ski motors, they use a star shaped rubber damper between the crank and the driveshaft:
http://203.89.255.42/pic/22s/3050594_1_md.jpg
theres an alloy piece on each side that grips the damper, and are screwed in on the crank & driveshaft in the direction the motor turns. in other words, after 25 years theres just no way to get it off, i tried with 3 people and a blowtorch and metal levers and all the bolt loosening fluids i could find and i gave up cuz i was gonna break the flimsy allow pieces.
what this means to you: you will need to find a driveshaft and get a $45 rubber damper online or pay $80 locally