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I have been working with Adobe After Effects now for over a year, and I can honestly say there is not a lot this piece of software can't do.
First of all, I run After Effects (or 'AE' as I'll refer to it from now on) on the most basic of the Macbook Pro range and despite common misconceptions, my system is perfectly capable of running the software. AE is very versatile so you don't need a 12-core Mac Pro to run it. All that is needed is maybe previewing your renders in half or third quality (since full quality preview renders are almost never necessary) or preview rendering in smaller sections. So I just wanted to start with this to dispel any fears that your system won't run it. It probably will.
AE is compatible with many different file formats and will accept and export to almost any format you would want. If you already work with other Adobe products such as Photoshop and/or Premiere Pro, then AE is a no-brainer. AE is extremely compatible with other Adobe products and you can directly import Photoshop files and export for Premiere pro which means less rendering and less quality loss.
I could go on forever talking about everything After Effects can do so I won't go on, however if you are new to the software and are deciding between this and some other software such as Apple Motion, having used both I can safely say that AE's interface is much more logical, user-friendly and easy to learn. The only circumstance under which I'd reccomend Apple Motion as opposed to AE would be if you are already familiar with Final Cut, or intend to import your files into Final Cut for editing.
Also, this software is offered for a reduced price for students directly from Adobe's website, so if you are a student of prospective student it is definitely worth taking advantage of this.
Overall I would highly recommend this software. It is industry leading and has a relatively simple to learn interface in comparison to competitors. The only reason I would advise against this software is if you are very competent with Apple software or have a heavily Apple-centred workflow.
One final note, if you are looking to learn this software I highly recommend visiting VideoCoPilot.net and viewing the basic tutorials. They are free and provide an excellent platform for exploring the hundreds of other tutorials the website has to offer. This site provides the best training you will find anywhere.