Even the car radio type coax would probably have too much capacitance
for the length of run you'll need. Yes, you could put a preamp
(actually an active impedance converter) near the antenna in order to
drive standard 50-ohm coax cable. I classify it as an "impedance
converter" because you probably don't need or want much gain, just the
ability to match the coax impedance. On the broadcast band any gain
will likely increase the noise level as much as the signals.

If you don't have too much noise pick up from the house electrical
wiring, etc you can probably just run a single wire feed line down
into the basement. Keep it as far away as possible from any conductive
material like rain gutters, etc.