I would like to purchase a nRF24L01+PA+LNA (http://www.ebay.com/itm/321145353149
), which allows for long range communication (~ 1 km). If I use this as my transmitter, do I also need a nRF24L01+PA+LNA as my receiver, or can I just use the less expensive nRF24L01 (range only 100 m) to receive the signal from the nRF24L01+PA+LNA?
If reliability is important then yes. Those devices do handshaking when they send data so communication is <b>always</b> two-way.
You can turn the handshaking off if you don't mind lost data but you probably still need it for anything over 100m. The difference in price is only about $8 so why risk it?
PS: A normal nRF24L01 can only do about 10m, not 100m. I'd be very surprised if one can do 1000m even with an antenna unless you're out in the countryside away from everything electrical and with perfect line of sight (what do you want for $11?)
The only time I wouldn't use an antenna is if the extra weight is critical, range is under 100m and lost data packets don't matter - eg. RC aircraft.