I think pretty much any machine-washable clothes can be washed in a top-loading washer, as long as it has a cold or a gentle setting. Just check the labels on your clothes. I've used mesh bags in top-loading machines with no problems too.

My old apartment complex had the high-efficiency washers. I can't remember exactly how long the cycles were, somewhere between 20 and 25 minutes, and I never had problems with my clothes not getting clean. I mean, I wasn't covered in mud or anything, but they always got my stinky workout clothes sufficiently un-stinky.