What branch of game development should I go for?

Not to burst any bubbles, but after 10 years of industry experience I'd recommend first watching this video and seriously considering all arguments against, and reevaluating all your reasons for attempting to get in:

[So you want to work in the video game industry] https://youtu.be/lGar7KC6Wiw

Br prepared to start at the bottom and work your way up. It can take years at very low wages to one figure out what you want to do and develop appropriate skills toward what you want to do. You will sleep eat and dream in spreadsheets.

That being said take a look at universities with game design programs, because they didn't really exist quite as much as they do now until about the last 5 years. Consume and pick apart games you play, check out even more classic games and any indie games and be ready to list the key selling features, game mechanics between them. Design games on paper, test them out with friends and iterate over and over to work out problems and balance.

Music is (I'd say) a harder than normal angle to get into, as usually a company has one or two audio experts, and use 3rd party vendors for both implementation and source. If you want to go that route you'd probably want to intern/go for starting level positions at music production studios for years before attempting to make the jump into the games industry.

My best advice is to get a well rounded education. You may find inspiration leading somewhere else in the process, but it sounds like aside from programming and traditional+3d art, your path is toward design or something else (up to you to figure out). A degree in design these days may help, but unless you land an internship it will be very difficult to get your first break(be on the lookout and be prepared to have a portfolio). That being said there's nothing wrong with starting out in testing. Most designers I know started with me in QA. It took 4 years at as many companies to figure out and get a chance at the next step.

The games industry is an ever changing and volatile place. Many companies are chasing what's currently best selling and established only to crash and burn(5 years ago it was WoW, now it's LoL). Companies rise and fall and so even with a successful career expect to move around, and be subject to semifrequent layoffs. I've found after my first 3-4 years it's about the professional connections you make as much as it can be about skill if not more, that can lead to you getting your next job after a layoff.

/r/videogamedev Thread