i’m not familiar at all with the handycam, but if you can get control of the iris/apperature and the shutter speed/angle you can make you footage seem more film-like.
a more shallow depth of field is common in film, and can be attained in video if you can open the iris or apperature to give you a shallow depth of field. if you are shooting in brightly lit areas, this becomes more difficult. in film they could just use a slower film speed, but in video you will need to use neutral denisity filters to be able to stop down the apperature. you may be able to find a filter adapter for your camera to utilize standard filters.
a normal film shutter angle would be 180, that would equate to a shutter speed that is double the frame rate. so 24fps would have a shutter speed of about 1/48 of a second. so for a film-like motion blur you would like to set your camera to use a shutter angl of 180 or a shutter speed of double the frame rate (standard video is 30fps, so a shutter speed of 1/60 second would be more filmy).
finaly, in ae you can deinterlace your footage… i wouldn’t try to go from 30fps to 24fps, (unless you handycam can shoot 24p) but even taking your 60i to 30p will seem a little more film-like, and if you were able to shoot with a shutter speed of around 1/60 it should look very film like. there is a preset in later versions of ae called ‘reduce dv blockiness’ that can help lessen dv artifacts, there are also procedures here and on the web. adding a little grain can help hide dv video artifacts too. you can also look for color treatment tutorials, if you want to mimic a certain color processing treatment in used in films.