Hard to answer without knowing what you have there already. Those rooms definitely need ventilation but I don't usually see that ventilation being part of am interior door I imagine you could put on basically any solid core that fits.

Also Chicago has a history of unique and expensive antique door hardware so if your house is old you might want to do some googling of your knobs, lock sets, and hinges and either donate them to a place that deals in antique house parts or sell them online.

Replace what you have with similar is usually logical. Modern laundry usually has a vent, so at least a gap at the bottom of the door is necessary. Furnace room will have more important code requirements. Old furaces and water heaters drew air from the room. That's no longer allowed in new appliances. So if they do draw from the room, you must have ventilation. If not, it doesn't matter / isn't required. Either way, that doesn't prevent you from installing solid doors. Also, you can vent through the interior wall if you don't want to cut into your door.

I’ve just finished replacing all the doors in my condo and another thing to keep in mind is fitting the exact dimensions. If you’re going pre-hung you should have more flexibility, but if you’re keeping the door jambs and just getting new door slabs then you’ll want to measure very precisely. I assumed mine were close enough to standard widths 24”, 30” etc. and they were slightly smaller so I ended up having to trim a quarter inch off the doors to make them fit.

I'm curious why you are replacing all the old doors. Is this an aesthetics thing? They can't be painted?

For the furnace door, you probably need a fire-rated door. Finding that information can always be tricky. Calling townhall can open up a can of worms. Asking at a big box store, you'll get a bunch of clueless workers.