There are many apps for making graphics, but you should really take time to study the differences between then to see which one will accommodate your workflow the best. For Example, many designers I know rely on Fireworks as their go to art app because of the variety of publishing avenues it has. Heck, I tend to use it for frame by frame animations in it myself. I have the full Adobe suite but hardly use Photoshop but say for when I need it for rasterized trickery.
It really depends on your familiarity with these tools and yes, artistic skill/education. If you have some money to invest, go with a Pro-level graphic app and invest in some time in some tutorials. You'll likely get a lot out of just studying and following along with videos /tuts on sites like Lynda.com or cartoonsmart.com
Can you do OK art/drawings/graphics with pen and paper?
If yes, and given that you are just starting out with digital art, try Inkscape first. When you're finally comfortable with the tool, then start to decide if you want to remain with Inkscape or use other "more advanced" tools. I don't personally use it, but Inkscape seems to be professional enough for many senior graphic artists to use it for actual work.
If you want to stick with simple 2D-esque work, you can move on to Adobe Illustrator. If you want more textured/polished effects (e.g. for faux 3D/realism) you can go with Photoshop. Ideally, it's a combination of the 2 + software like Anime Studio for animation.
If you can't hold your ground with art though (nothing wrong or degrading with that) you can always hire artists to work on your game's art for you start with artist friends first, then when you're comfortable with the art of commissions you can move on to pros -- try Deviant Art's commissions thread, or in the GS Forums.
There are so many programs, you have is to find out, the one that seams more easy for you to work.
Start by "InkScape" is free, and very easy, just give it some time to discover how it works. For example, my games art had been made on: Inkscape(Win,Mac), Paint.Net (windows), PowerPoint(windows)...
You could also look at pairing up with an illustrator. You could pay their full rate and own the art work or work for a reduced rate for a split of sales. It's hard to wear all the hats and having a few illustrators you can pair with could work out for you. Best of luck
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Artist/Game Developer / Animator at your service..
It really depends on your familiarity with these tools and yes, artistic skill/education. If you have some money to invest, go with a Pro-level graphic app and invest in some time in some tutorials. You'll likely get a lot out of just studying and following along with videos /tuts on sites like Lynda.com or cartoonsmart.com
If yes, and given that you are just starting out with digital art, try Inkscape first. When you're finally comfortable with the tool, then start to decide if you want to remain with Inkscape or use other "more advanced" tools. I don't personally use it, but Inkscape seems to be professional enough for many senior graphic artists to use it for actual work.
If you want to stick with simple 2D-esque work, you can move on to Adobe Illustrator. If you want more textured/polished effects (e.g. for faux 3D/realism) you can go with Photoshop. Ideally, it's a combination of the 2 + software like Anime Studio for animation.
If you can't hold your ground with art though (nothing wrong or degrading with that) you can always hire artists to work on your game's art for you
Good luck!
Start by "InkScape" is free, and very easy, just give it some time to discover how it works.
For example, my games art had been made on:
Inkscape(Win,Mac), Paint.Net (windows), PowerPoint(windows)...
Start with the earlier posts and go from there: http://2dgameartforprogrammers.blogspot.com/2011/10/lets-get-started-with-circles.html