Are residential proxies detectable?

In the case of a residential proxy, how would the signal travel from the remote location to the monitoring location?

I'm assuming it would be in the microwave frequency range. You could use VHF or UHF in the 300-500 MHz band (300 kHz - 500 kHz). They could be used to create one-way links between the two places over the distance you're considering. You could put the two stations on either side of a narrow mountain or cliff and set the frequencies accordingly. You could use the ham radio bands. The US and EU ham radio bands can cover several miles and several hundred kilometers, depending on whether your transmitter is an "aerial", "mobile", or "land". With low power antennas and transmitters it's possible to reach a mile for a good aerial, several miles for mobile, and a few kilometers for land use. And in some situations there areas where the radio horizon doesn't follow the physical horizon.

There are also other methods of long distance signalling - Morse code, HF CW, HF PSK, and the various forms of spread spectrum methods like LPD. They can be more flexible and offer more bandwidth than radio, but they have tradeoffs.

I don't know if you're going to need that much bandwidth. If your distance between the two is less than a few hundred meters then radio will be much more effective than using spread spectrum techniques.

What are the best proxies to use?

I would go with Google, because it's the most known.

Other options are: Ask Jeeves. Yahoo! Bing. Most people would be familiar with Google, but in my experience Ask Jeeves has much better search results. It is also free (as opposed to Yahoo which is not) and has more features. I have used both, and if you are only doing text searches, I would recommend Ask Jeeves.

Use google as a proxy for Google. It will be faster and most likely give you the best results.