Web design

Web designing is a promising career opportunity, which displays immense scope for interested candidates. In India, it is one of the biggest industry, which provides a possible room for web designing as a career opportunity is the IT or the software industry.
They also welcome fresher, who are put through rigorous training and then made to learn the ropes under the wings of the experienced seniors. This provides them with an excellent opportunity to learn the work hands-on.
Most organizations also recruit web designers for their internal projects, which have a distinct flavor of their own as it provides the opportunity for designers to interact with major company stakeholders, who run these internal initiatives.
Web designers are also required in the media industry like news or advertising agencies or even in the education industry, developing educational websites and learning material for students.

I think you must go for full-fledged animation course because animation is very vast field. In full-fledged course, you have graphic designing first then web designing, 2D animation, sketching, 3D modelling and 3D animation. Also, you have many software to go through while this course. These courses generally last from 2-3 years. If you have already decided that you want to become only graphic designer or may be web designer, you must go for only those plan only no need to take full-fledged course. But, I personally prefer you to go for full-fledged course. Because as you go through the course, you will develop other interests also which you may like and don't know right now. So, all the best.