I don't see anything to keep you from using the Bose speakers with another receiver. It may involve getting different speaker wires than what Bose supplied, though.You will want to make sure the new receiver can do a fairly high crossover from bass module to sats, though. Some receivers will only allow you to set the x/o at a few points, with the highest one being maybe around 150Hz. The Bose system should probably x/o above that. Maybe 200 Hz. And btw, in spite of what one of the resident experts said, the Bose Lifestyle 12's bass mod is powered; not passive.
As for which surround receiver you get for them, I would just compare then all and make my choice. Within a given price range, there is going to be more similarities than differences. Personally though, I like Onkyo.