I'm not sure I understand your difficulty shifting your current bike. There's really not much to "knowing how" to do it. I would almost bet that something's not adjusted right and that's what's making it difficult to shift. If you get a new bike, my guess is that you'll be amazed at how well it shifts by comparison. I don't know much about the chainless drives but I would recommend dropping that as one of your criteria because you're going to severely limit your choices. I think a good quality folder might be a good choice. Dahon and Bike Friday make some good folders.

http://www.dahon.com/

http://www.bikefriday.com/