I can only suggest you look at some of the pre-existing applications in this frequency range. This is over a decade of bandwidth you want to cover.

Loran (~80 kHz) uses a whip antenna. Enclosed in the base is a band filter and amplifer which is powered by DC on the coax.

100 kHz is a somewhat unknown experimenter band. You might find articles on this.

Up to 550 kHz used to be used for aircraft radio direction finding. Steerable loop antennas about 1 foot diameter used for old sets like the ARN-6 and ARN-7

550 to 1750 - AM radio. Ferrite loop/stick antennas are common.

~1.8 MHz is the Amateur radio 180 meter band - a somewhat obscure amateur band. You might find some antenna articles.

Active whip (typically a whip fed into the gate of a FET). Pretty much omnidirectional if the whip is vertical. SNR is generally set by the external environment anyway, so there isn't much that can be done if you want omnidirectional (except to try different polarities and relocate the antenna itself).

Loops are generally directional. Using two combined at RF is still somewhat directional.

Radio compass (ADF) antennas used on aircraft are exactly what you are looking for.  They cover 150KHz - 1.6MHz in three bands (from memory).  They have a ferrite antenna for the directional component and a voltage probe whip for the omni component.  

They actually have two ferrite rod antennas at right angles to give crossed fig-8 patterns and you could do the same if you want ferrite and omni directional although it might be useful to have that fig-8 pattern that a ferrite antenna gives to null out interference.

It is best to tune the inductor on the ferrite rod to resonance to reduce losses and improve noise rejection.

If you don't have to have ferrite then a voltage probe is a lot easier although it's still a good idea to tune them.

I forgot to add, check thread 247-156809 which discusses voltage probe antennas.