Doing a further research within LinkedIn Animation groups here, it turns out that the program SoftImage XSI is now Toonz and it is used by Studio Ghibli for their productions. This is especifically their Story Planner PRO software:
There are a whole variety of 2D and 3D animation programs out there for professional-looking projects. There is really no standard for the industry, but rather certain programs that certain studios and people use.
For example, a popular program among digital animation students is Digicel Flipbook and also TV Paint.
Another great program is Plastic Animation Paper, or PAP. If you want an organic paper and drawing, classic feel, this is it for you. The PRO version is FREE! http://plasticanimationpaper.dk/ However, this program doesn't have the technology to color your animation, but it's great to achieve basic traditional animation easily.
Whereas Toon Boom has been used by American studios such as Disney, Warner Bros, Cartoon Network, Cookie Jar, O Entertainment, Film Roman, Fox, etc.
But if you want to keep it simple, then Adobe Illustrator along with Adobe Flash can be the route to go. There's plenty of tutorials available in torrentz sites that may help you without spending a dime, and it will let you have the knowledge to achieve what you want. You can add special effects later with Adobe After Effects.
If you want to especifically create anime without much hassle, then SmithMicro's Anime Studio Debut or Anime Studio Pro can be the best option. They are the same developer of Manga Studio Debut and Manga Studio EX.
The most important thing that you should keep in mind is that you can use any of these programs, as long as they feel comfortable and manageable. No program is really better than the others. The main idea is to achieve the exact results you want in your project :)