The antenna you want depends on your application. To start with, there are two classes of antenna: omnidirectional (where the signal radiates out from the antenna with equal strength regardless of the angle you are from the antenna feed point) and directional (where the signal is stronger in one direction than in other directions). If you have a fixed transmitter and a fixed receiver, then you'd want directional antennas pointed at each other. If you have a moving receiver or transmitter, then omnidirectional antennas will be easier.
After that, antennas have orientations: they can be horizontally polarized, vertically polarized, or circularly polarized. In general if one antenna is horizontally polarized and the other is vertically polarized, you'll get signal loss.
A half-wave dipole is a simple antenna. It consists of two equal lengths of wire, each 1/4 wavelength long (approx; start a little longer because wire is not a perfect conductor). One wire is connected to a coax centre conductor and the other connected to the braid. Here's a picture:
If you mount it vertically, it will be omnidirectional. If you mount it horizontally, then it will be directional broadside to the wire (it won't see a signal that's at the front or back of the wire).
Here's a picture of the radiation pattern of a horizontal dipole. It will see (and transmit to) everything in the two circles:
A 1/4 wave vertical is half a dipole, mounted vertically. The other "half" is a surface that reflects radio waves in the same way that a mirror reflects light waves. Because it's tricky to make a vertical 1/2 wave dipole (with a feed point halfway up the antenna), people often make a 1/4 wave vertical with the feed point at the base, and the coax braid conducted to conductors running flat along the ground to act as the reflector. The reflector is the ground plane. Often, rather than have a perfectly flat conductive surface, people use a number of wires radiating out from the centre.
Here's a picture of a vertical:
To start with I'd avoid adding coils and capacitance to your antenna. Also, be aware that metal objects near the antenna will change its radiation pattern. Get them as clear as you can (typically 1 wavelength). If you can't do that - not a big deal, you just might have "dead zones" (nulls) that aren't in a typical dipole or vertical.
Thicker antenna wire won't do much for you on a fixed frequency application. (It could give you a better bandwidth if you have multiple receive frequencies.) The coax won't make too much difference at the power levels you're using as long as you keep it short.