Although if you just use the generic 个 for everything besides (formal) people, people will understand what you're saying and give you a pass for being a non-native speaker.

At this point for me, the measure words are actually a help instead of a hindrance when I encounter a new noun that I don't know -- it hints strongly enough at what sort of noun I'm dealing with that the context usually allows meaning to more readily snap into place. More useful than memorizing generic masc./feminine/neuter for most Indo-European languages.