Hi Elke,
Turnstiles and luggage do not mix... at all. You will have to lift and hug your baggage to your chest if passing through a true 3 prong turnstile. Luggage passthrough holes (see extreme right hand side of photo below) can be found at
some stations, but definitely not all. Using the handicap barrier is the best bet. Just remember to wait patiently for the gate to open! It will be slow, taking roughly 5-6 seconds to start opening after you've validated your ticket or pass.
For double door swinging gate barriers (like those in the picture below) that some stations now use, you can pass through with a suitcase about 24 inches wide. You may have to pull your suitcase
sideways through the gate (so that it is as narrow as possible in terms of width). Do not take your time when doing so! There are infrared sensors on these gates that tell the barrier when to close. People who walk through these gates slowly give the sensor time to notice a gap in between their body and the suitcase in tow, resulting in the gates closing on the suitcase and blocking it. These gates are quite strong and you'll need to put a bit of effort to remove your suitcase. If the gate has close on the extended handle part, rather than on the body of the suitcase, it's a lost cause, you will not be able to force open the gates without heroic strength (or help from passers-by).

Hope this helps, Elke,
Ben