Yes it's a good idea to manually move what you need. You will probably have things installed you forgot about & don't need to migrate.
Yes you can just sign in to the App Store with your Apple ID & download all the compatible software you own. It's best to download any apps again so that you get the latest versions. Make a list of what you use & check roaringapps.com for compatibility info.
You can use Migration Assistant to just copy the user data if you want, however that can bring old preferences & other cruft.
Run EtreCheck if you want to see what is running on the old iMac.
Print it out & show the assistant if it is full of kernel extensions & launchd items. You don't want them on 10.9 unless you actually use them.