Does the antenna type matter for receiving?
It makes sense that I would want something specialized to transmit data. My question is if I need such an expensive antenna for receiving,


The transmit and receive antennas are equally important for determining the signal amplitude delivered to the receiver electronics.


  I have noticed that high-gain SMA antennas are quite expensive (about $5) as compared to just regular wire.


In the world of antennas, "high gain" means that the antenna has a highly directional emission profile. It does not mean that the antenna is able to deliver more power into the transmission than it is provided by the amplifier that drives it.

If you want to be able to transmit or receive signals without knowing which direction the other station is in, you do not want a high gain antenna.

If you know what direction the other station is in, and can point the antenna toward it, then you want a high-gain antenna.

More likely you want to find an antenna with good electrical efficiency at the frequency you will be using. Again, the transmit antenna and receive antenna contribute equally to the overall efficiency of the link.