Graphic / Web Design

There is nothing called the best subject, as it will differ from person to person's interest.
Find below the list of subjects that are taught during graphic designing:
1.Genetic skills
2.Typographic Design
3.Computer Studies
4.Basic Information
5.Color Theory from Computer
6.Graphic Principle and method of design Introduction to Multimedia
7.Digital Publishing
8.Visual Communication
9.Sound Principles
10.Introduction of computer animation
11.Modelling using CAD
12.Multimedia Authoring
13.Digital Portfolio Development & presentation
14.Web Design
15.Flash & Scripting for Web
16.Principles of management
17.Web campaign Implementation
18.Drawing as Basis for 2D and 3D Animation
19.Design: Character
20.Background & Concept
21.Animation the production process
22.Composing/shooting on film
23.Sound recording breakdown: Voice
24.Music & Effects film
25.Language career planning and guidance
26.Team Management

Hello,
Most of the graphic design these days are digitalized. You need to have a proper understanding of pixels, colors, patterns, algorithms, etc.
You can learn these separately taking any subject. But if you are sure if want to do graphic designing, this comes as a very niche segment in computer design.
You can go to colleges like NID (National Institute of Design)
Science will be helpful in this front. You can also go for computer engineering and post that do Masters in graphic designing.
For this also, you need to have science. This highly depends on the level you want to achieve. You can learn graphic designing while studying any subject in parallel.
But to have a deeper dive into the concepts choose science then try for computer engineering followed by Masters or NIDs, etc.
All the best.

Your question is exactly on career and job segment. According to my experience, there are lots of career scope in animation and VFX field. Animation and VFX is biggest part of Media and Entertainment industry.
Accordingly FICCI report, Media and Entertainment Industry is highly growth field right now.
The Federation of Indian Chambers of Commerce and Industry (FICCI) is an association of business organizations in India.
The media and entertainment industry in India consists of many different segments under its folds such as television, print, and films, radio, music, OOH, animation, gaming and visual effects (VFX) and Internet advertising. You can work all these segments.
In these segments, you need just understanding of software skill, tools of the industry no further requirement is needed.
As per the combined survey report by KMPG and FICCI, the entertainment industry in India is expected to expand by 12.5% every year and is likely to reach US$20.09 billion by the year 2013.
The industry is estimated to achieve growth of 13 per cent in 2011 to touch US$16.2 billion. As the industry braces for exciting times ahead, the sector is projected to grow at a CAGR of 19 percent 2020 which is highest growth as compare to other fields that mean more income and jobs.
In MNCs like Pixar, Technicolour (Bangalore), Rythm and Hues (Hyderabad), Red chilies, Prime Focus, DQ entertainment etc. salaries are more than software engineers.
If you are interested in this field so you can just join a professional career based course in best institute no degree is required in this field, because I have already mentioned that Animation and VFX depends on creativity and software skills.
For more information please visit:
https://www.shiksha.com/Maya-Academy-Of-Advanced-Cinematics-Chandigarh-institute-college-listingoverviewtab-37864
http://indianexpress.com/article/entertainment/entertainment-others/indias-animation-industry-has-seen-unprecedented-growth-avneet-kaur/
http://www.animationxpress.com/index.php/latest-news/animation-and-vfx-industry-to-grow-by-8-5-per-cent-and-18-5-per-cent-respectively-by-2020-ficci-kpmg-report