A Turn Indicator indicates that the aircraft is turning, i.e. its heading is changing, a Slip indicator indicates that it is slipping, i.e. that its nose is not pointing in the direction of travel.
A Turn Indicator is generally some form of gyro, mounted such that as the aircraft changes heading, the gyro attempts to point at the same bit of space which exerts a force on a "suitable series of springs and levers" that then moves an indicator on the instrument face.
A Slip Indicator is a ball in a tube that slides out to one side or the other depending on which way the aircraft is skidding, or a piece of string stuck on the windscreen of the aircraft that gets blown one way or the other by the air stream hitting the aircraft's nose.
As for avionics - sorry, no idea. But the Garmin 430 does look good in the ads (and Pilot magazine had a review of one recently, very favourable).