spl, I have to make lots of assumptions here, you describe your system in very generic terms. I am going to assume your RTL box has two input connections, both accepting Type F connectors, the kind used by TV cable boxes and 75 ohm coax. Or they could use SMA connectors, a smaller size. Change my answer to suit your conditions.
100 KHz to 30 MHz 66 feet is not a magic number for what you are trying to do. The distance you need is what you have available. You are looking for a broadband antenna, not something for just ham radio frequencies. Speaker coil wire is really fine, and not very strong. Connecting it to a tree will break it when the first good wind moves the tree limb. You want to tie the antenna wire to a thin cord and run this through a pulley, attached to the limb, and down to a small weight. Then when the tree moves, the cord can move, keeping the strain on the wire more even. 22 AWG insulated, stranded hookup wire is stronger, and not expensive. The impedance (the AC electrical resistance of this wire) will change greatly over the frequencies you want to receive. A company called Noolect (nooelect.com) makes a barebones 9:1 balun/unun that can convert the impedance seen on the antenna wire to something more acceptable to your RTL. (or coax). This will give you a stronger received signal. For what you sound like you want to do, if it's not inconvenient, just bring the wire in a window, and connect it to the 9:1 and then through a short piece of coax to the RTL. You can get fancy later, routing it through a vent if it seems to work ok. All antennas have two parts. Two wires in opposite directions for a dipole, or a wire in the air, and the ground ( earth surface) for a monopole ( single wire) antenna. If you are near a window, and can run a 8 foot wire to a stake in the earth to your radio, great. If you have your 9:1 balun outside, and can ground it with a short wire to earth, great(er). The radio wave travels to the antenna wire, through the front end of your receiver, and then to earth. If you can make that path a lower impedance, then the received signal will be stronger. But if you can't, the wave will travel through other paths to ground, just not as strongly. You have at least two other options, Google e probe antennas, and loop on ground antennas. One of those types might strike your fancy. PART 2 The VHF/UHF part I can't speak to very much, locate you antenna up above the roof line if possible, Vhf/Uhf frequencies are very susceptible to shadowing by structures. The Nagoya whip is really designed for ham radio frequencies. A better broadband antenna is called a discone. Tram makes one for about $70. There are others. You might want to research that also. Good luck in your research.