I wholly agree with the other answer which says that you could just get quality tap water from the staff or something like that.
However, for this answer I’m doing something I often do, which is accept the premise of the question itself, which says “I want a device to remove the following substances from water.” I am assuming (wrongly or rightly) that is a justified premise, and answering that.
Considering the substances that need to be removed, I’d say that this can not be accomplished by simple filters. As references for this statement, see answer 1 and answer 2.
You need either a distiller or reverse osmosis.
Incidentally, both these methods also remove pathogens, so there will be no need to additionally boil the water.
Reverse osmosis accomplishes this by pumping water through a membrane with very tiny holes. A good RO system removes everything you are talking about in the question. Here’s another answer in which I mention an RO system that is portable and can be connected to the tap through a hose, eliminating the space concerns.
You mention chlorine in OP. Please note that the higher the chlorine level, the more of a strain it will be on the membrane of the RO system. (For normal, municipal water chlorine levels, it’s not a problem, though.) But the higher the levels of chlorine, the more often the membrane will have to be replaced.
Distillation works by creating steam and collecting the steam as water. Since none of the chemicals or pathogens you mention will evaporate in the steam, they will be eliminated in the distillation process. Here’s a related answer in which I describe distillation in further detail. With most distillers, you manually pour the water into the distiller using a jug or something like that. Thus, the space is not a problem there either.
Please note that distillation is quite energy inefficient compared to RO. It uses a relatively high amount of electricity, whereas RO does not.