Yep, sounds rignt... Dunno where you went wrong, or what teh problem is...

spinner back plate (with appropriately sized 'shim' to fit teh prop shaft, and the TE of teh prop blades against teh little nubs / stops)
prop
thrust washer (that thick washer)
lock washer (split type, BUT ONLY IF IT FITS. Some people / insurance bodies (MAAC) reccomend you put one on. Added safety. BUT make sure, that when all is tight, there is still about 3 threads on the prop shaft showing)
then snap on or screw on teh spinnner itself!

there are different plastic spinners, adn they more or less lookand wiork teh same. Some snap in place (Goldburg I beleive) and soem need screws (Du-Bro)..

Aluminum spinners (Tru-Turn, GP) require an 'adapter nut' which replaces the prop shaft nut. The spinner securing screw screws into this adapter, from teh center of the spinner.