Habib,
Because you are just getting started, it is best if you choose a design that lets you develop your skills and avoid catches. A vase is a closed form meaning that the opening is narrower than most of the vessel and this shape greatly raises the possibility of making a catch. Whether you’re doing open or closed segments, an open form is a much better choice for getting into segmenting.
If you are going to make a closed form vessel, it is a good idea to do some turning on the inside as you go. Add a row or two and then use a bowl gouge. A fingernail gouge if a special purpose tool that is useful for adding sharp detail - mostly to spindles but it has very little usefulness to turning the inside of a bowl and will likely result in catches.
To turn the inside as you go, add a ring or two and then use the bowl gouge with the handle far to the right so that only the tip of the gouge will be touching the wood and you will NOT be riding the bevel at this point. Push the tip into the wood towards the base of the vessel, removing a very small amount of wood. This will allow you to remove the wood that will most likely catch and let you establish a surface that can then allow you to ride the bevel to let the bowl gouge work as it was designed..
If you are making an open segment bowl, you want to avoid any turning of the last row you added because it is not locked into place until you add a new ring above it and then it turns like a closed segment ring.
I’ve attached a picture of an open form shape that I do in my workshops that can be either a open or closed vessel and it gives you good turning experience and let you successfully complete a turning and this initial success is very important.
Finally, hang in there! Every one of us has been in the same spot as you are today. Fortunately, getting over the initial hump goes fairly quickly and you will soon develop the feeling that tells you that you are on the verge of a catch. Sometimes you can hear it coming, sometimes you can see where it will happen, but you can always feel that a catch is possible. When you get that feeling, stop, and consider the tools you have and which one can handle a difficult situation.
Lloyd