Here is a basic cheap
no-name POE camera.US-Amazon link
Near price point you mentioned.
With no POE Equipment you need to consider the options.
Cheap POE router like
TP Link ~$40. That will serve many cams.
-Versus-
POE Injector for single cam. That is cheapest option. Maybe $30
POE+ brings higher amperage and voltage allowing for really long runs.
Arecont is a good brand POE Camera that are costly but there are ebay deals.
If you care about your outdoor equipment get a POE ethernet lightning protector.
If your looking for absolute cheapest there may be an balun for that. Analog cameras only.
2x adapters included CablesOnline Part Number: BL-101-2. BNC Male connector. These adapters are a simple and inexpensive way to make long video runs using UTP cable as opposed to the more expensive BNC coax cable.
www.ebay.com
Might need to inject power with something like this and a wall wart:
Supports 5V, 12V, 24V, 48V. PoE Injector + Splitter Kit. Quantity: 1 Kit = (1) Injector + (1) Splitter. Splitter: RJ45 Female to RJ45 Male + Power Out. Injector: RJ45 Male + Power In to RJ45 Female. Can work up to 150ft (depending on the quality of the cable and the power draw of the device).
www.ebay.com
You would also need to test your wiring carefully here on the cheap approach..
Also you need to digitize this analog signal. Video capture.
Zoneminder does not do analog anymore nor BlueCherry.
Motion works with Bt878 cards.
Whereas POE is plug and Play.
Some vendors play games and offer 24VDC POE..
POE is 48VDC and POE+ is 56VDC. Anything else is out of spec.
Webcams are all USB and the reach there is only 70ft with extenders.