I would suggest a Rinnai Energysaver. Probably an EX22 or EX 38. It is a direct vent unit with modulating gas valve and blower. Programmable t-stat is built in. Cool to the touch and QUIET! There are vent extensions available to bet the vent to the outside. I ran one in my basement for 10 yrs. Mine was not a finished basement but many times I would turn it on Fri evening in preparation to spending the weekend in my basement shop. What I found was that like yours I did not have an insulated first floor. The Rinnai would heat the floor and it actually would change the comfort on the first floor due to the basement heat heating the first floor. I have heated my homes with these units since 1991. They are excellent?

I am sure that those are great units. And I am fine spending the money if I need to, but that seems a fair bit of expense just to heat 400 square feet 5 degrees.

How is the rest of the house heated? Your basement must get very cold during the summer with two AC vents cooling a 400 sq. foot area.

It doesn't take many BTUs to keep a basement warm. If you want to keep this simple and low cost then install the electric base board heat. For even less money you can buy two free standing units and put them at opposite corners of the room.

I realize heating with resistance heat is the most expensive operating option, but I assume you are not going to be heating the basement 24/7. A basement has a low heating load so the annual heating costs should be reasonable. It also makes sense to go with the inexpensive option if you have a potential of another flood.

"I am sure that those are great units. And I am fine spending the money if I need to, but that seems a fair bit of expense just to heat 400 square feet 5 degrees."

They are not cheap by any means, but you get what you pay for. If you were to economically heat the basement, how would that affect the use of the basement. I suspect it would be used more given that it is comfortable. For the 400' I look at an EX11 0r EX17. The 11 has some limitations on vent extensions depending upon how high the vent has to go to exit the building.

The house has forced air gas. I am leaning toward baseboard heaters.

I want to stress that my main concern is not really cost rather economy. I have no trouble dropping 5 or 6 k if I will see use or significant benefit from it. One reason I am drifting away from the direct vent options is that it will be a single heat source in a room that is roughly 20 x 20 with no insulation between floors I am afraid I will just be paying money to heat the middle floor and one side of the basement with a less efficient version of my furnace in the winter and will fight against my AC more so in the summer. This is also why tile and baseboard heat are so attractive. They will be spread out in our close to the floor.