Liquidy?
Not the word I would choose. The cake should still be jiggly, but should be cooked all the way through, and not liquid even in the center. Unfortunately, the tooth pick test is not a great deal of help as a fully cooked cheesecake, even a cooled fully-cheesecake may stick to the pick.
If, when the cake cools all the way down, it's solid... you were fine.
Cool-Down:
Cool-down should be done slowly. Some people leave the cake in the oven with the door open, some slightly modify it by pulling the rack part way out (vestibule method). Others put the cake, in its pan, on a rack.
If it cools too quickly, it will crack.
After it cools, cover it and put it in the fridge to let it ripen. Overnight is better than all afternoon. At least let it cool all the way down to refrigerator temperature.
Hard for some people to conceptualize, but chilling is part of the cooking process.
Mixing:
Always soften the cream cheese (allow it to come to room temperature) before beating. Beat the cream cheese without anything else in the mixing bowl until it is completely creamy and smooth before adding other ingredients. Add your eggs and flour (if using any) last, and beat only until incorporated.
Beat at a lowish speed, all the way through the process. Unlike other cakes you do not want to get air into the batter.
It might help you to think of cheesecake as more of a custard than a cake. You want something smooth and silky, not an airy foam.
Hope this helps,
BDL