Advice on Replacing/Upgrading forced air gas furnace

Hello all,

Brand new to the forum and hoping for some advice. I came across this while searching for info and some of the responses that I saw posted to all were outstanding so I didn't hesitate to join (normally remiss about signing up).

Anyway, my current system is a Trane XE 80 forced air gas furnace that is tapped into old duct work, some of which is the old convection type for fireplaces/wood burning stoves in the basement (house was built in 1910 or so). The system has a Honeywell electrostatic filter, and I had the house insulated (blown in cellulose), and windows are relatively new (vinyl, double pane). Also, the kitchens and bathrooms have no heating (mother/daughter setup). I am looking to upgrade my system with the following goals/concerns:

Concerns (in random order):
- air is very dry
- temperature, while better than before insulation, still fluctuates too much
- two of my three kids have asthma, and allergens are a high concern
- have lived in the house 8 years, and not sure how old the system was when I moved - may be overly inefficient

Goals (also random):
- increased comfort/more stable temperature
- improved air quality/RH level
- add central cooling
- reduce energy use/ongoing costs (willing to absorb higher initial costs if the break-even point is reasonable)
- add heating to kitchen/bathrooms (something hopefully more cost effective than electric radiant to all three bathrooms)

I have been examining options and doing some research (how I came across this site) and have considered the following options:
- balance system, add registers, add system humidifier
- upgrade furnace
- add compressor, keep furnace
- add compressor, upgrade furnace
- add heat pump, keep furnace
- add heat pump, upgrade furnace

Any advice/guidance would be appreciated. I am starting to do my HW, but have no prior experience nor training on this.

Thanks,
Eddie