An inexpensive TV antenna is typically a loop of wire with a balun circuit to adjust the impedance of the antenna to the 75 ohm impedance of the TV.
Amplified antennas amplify signals all over the broadcast spectrum, and can help pick up signals. However, they can also over-boost the signals and make reception worse.
If you’re living close to the transmitter, you don’t need an amplifier. For example, most of the San Gabriel Valley is within ten miles of Mount Wilson, where most stations have their transmitters. So, generally, amplification may not help.
The best antenna I’ve purchased so far is the $3 flat antenna from the dollars store. It’s called the Luxtronic, and it claims to be an HDTV antenna. It’s been better than some of the more expensive ones.