At 0F outdoors (the
99% outside design temp for Joliet) and 60F in the basement, the above-grade portion of the uninsulated poured concrete foundation loses between 60-70 BTU/hr for every square foot of wall area, comparable to a wood sash single-pane window. For an 1850' basement, say a 37 ' x 50' rectangle, with an average 1.5' above grade, that's ~260 square feet x 60BTU/hr = 15,600 BTU/hr for the above grade section. Taking a WAG that the losses to the below grade walls & slab add up to about half that much, the basement's heat load is going to come in about 23-25,000 BTU/hr, which is probably on the order of 25-30% the total heat loss for the house. If you bought some reclaimed 2" roofing polyiso and insulated the wall with it you'd cut the heat load down to under 10,000 BTU/hr and the basement would coast along at 65F just on the distribution losses of the hot air HVAC units alone. There are a lot of details to get right when insulating a basement wall- I won't cover them here unless you think that's something you will be persuing.
If you're going to continue to heat the basement with a hot water heater, and NOT insulating the walls, it's probably worth investing in the smallest all-stainless condensing
Phoenix Light Duty, which has a 76,000 BTU/hr modulating condensing burner, isolating the potable water in the tank from the radiant floor loop with a heat exchanger, using 2 pumps. That way you will always be able to cover the heating load without impacting domestic hot water performance. The peak heat load would still leave more excess burner capacity for domestic hot water than most 50 gallon standard gas hot water heaters. In this sort of application the Light Duty (only light duty in commercial hot water heater terms) should last at least 20-25 years, and would deliver over 90% efficiency (though it's burner is too large to fall under residential EF testing.)
Heating a radiant floor with a non-condensing gas hot water heater results in destructive condensation in the center flue heat exchangers unless you design the system carefully, and at the duty cycle it would be running with the basement uninsulated it would shorten it's service life considerably. If you insulate the walls it might be more cost effective to go with a standard tank heater, and take measures to limit condensation in the water heater.
Tankless heaters don't modulate enough to make them worthwhile for heating 8000-25000 BTU/hr design heat loads, and the domestic hot water flow limitations make them less than perfect solutions for climates as cool as yours. You never run out of hot water, but it takes forever to fill a big tub, and they short-cycle like crazy serving high-efficiency clothes washers & dishwashers, etc. They're fine for some folks, not for others. They also require upgrading the gas line distribution, typically requiring a dedicated home-run of 1-1/4" gas line between the tankless and the meter, with no tees to other appliances. It may also require upgrading the meter and gas service to the house if the HVAC units are sized at typically ridiculous oversizing factors.