Vacuum every day. (Get a little cordless rechargeable one if that helps, you can get a cheap one for like $100. Use the big vacuum at least weekly if you have carpet.) Wipe all the surfaces down weekly. It sucks, it's hell, I've considered paying someone to come dust for me, but it helps.

A larger air filter will help - look for a tower-sized one - but you need to clean the filters weekly or so by vacuuming them off. Replace them when the unit tells you to (otherwise, it just pulls air around the filter instead of through, defeating the purpose of an air filter). Placing it closer to the center of the room helps a bit, since most air filters aren't high-powered fans.

And, yeah, change your sheets weekly. Even if you don't have pets, you shed.