First, as someone already stated, make sure you're getting heat to your basement one way or another when it gets down to freezing temps.
I am sold on the oil filled 'radiator' style. I have been using one for a couple years now and I like the gentle heat it puts out. The maint disadvantage is that they do not put out instant heat - it takes a little bit to warm up the oil. The second disadvantage is that there is no fan to circulate the heat, so I sit mine under the overhead fan in the living room. Works great. If no overhead fan, you might sit a small oscillating fan behind it. Mine has the tipover feature, a remote, can be set to a specific temp, and has both a 750 watt setting as well as a 1500 watt setting.
Note that you get the same amount of heat from all 1500 watt units no matter the size or expense. Having said that, it sure seems like mine puts out a LOT of heat for it's size once it gets going.
I also sleep easier at night when it's running, as opposed to some of the other types. It doesn't seem to get as hot (to the touch) so I don't worry so much.
My .02