Sorry... This forum is to discuss how the forums operate, not specific products
Go to http://forums.adobe.com/community/premiere and ask in the forum for Premiere Pro, or Premiere Elements (hit page down a time or two to see the link for Premiere Elements)
PS - PPro costs about $800 and PreElements costs about $100
I agree with John T., and would start in the Premiere Elements forum.
I can move your post to that forum, if you would like, but do not want to move it there, only to find that you had also posted it to that forum.
I will PM (Personal Message) you, for your instructions.
Moving this post to the Premiere Elements Forum, as that is a very good place to start your quest. If you get a lot of replies directing you to Premiere Pro, then we can branch it, or you can post a new one to that particular forum.
Let's get the ball rolling by starting you off here: http://www.adobe.com/products/premiere-elements.html?promoid=DJDWY
That explains what Premiere Elements is, and gives a little overview of its capabilities.
If you think that PrE will help you, then I would see the various tutorials on this page: http://tv.adobe.com/search/?q=Premiere+Elements
to see how some things are done in PrE. Until you have an idea of what PrE is, and some general comments on what it can do, the tutorials probably won't make that much sense. That is why I gave you this link second.
Also, there are several resources for learning PrE, and many are listed in this article: http://forums.adobe.com/message/3953827#3953827
Again, without the very basics on the capabilities of PrE, those resources might be a "step too far." That is why they are listed third.
When you have had a bit of time to explore, do not hesitate to stop back by this thread, with specific questions, on what PrE can, and cannot do. Someone will answer those questions.
PS - if you plan on doing anything with Still Images, you might consider the Photoshop Elements & Premiere Elements bundle. One is basically for editng Still Images, and the other for Video (but can use Still Images in the Videos). The price for that bundle is often about the same as the MSRP of just one of the programs - almost like 2 for 1.
Also, from your linked YouTube example, there is Vector Art being used. Photoshop Elements can do a lot of that, but the ultimate program would probably be Adobe Illustrator, which is a Vector Art creation/editing program. Also, rather than Vector Art, Photoshop Elements can do a lot of such illustrations via pixels (Raster Art), and for doing an animation going to Video, might be more than adequate.
Premiere Elements has limited "drawing" capabilities, via its Titler. One can do quite a bit of illustration with it, BUT it is not really designed for illustration, and is more suited to add Text Titles to Video.
If full control of illustration is required, for the creation process, then Adobe Illustrator would be the ideal, but it comes with a bit of a learning curve, as most people initially think of "drawing," like with markers and paper, and Vector Art illustration, while offering much more control, is a bit counter-intuitive, at least in the beginning. If one decided to go with Illustrator, and the end result would be Video for say YouTube, then it might be worth the investment to look into the Adobe Production Premium (http://www.adobe.com/products/creativesuite/production.html?promoid=JQCRO), which contains Illustrator, Photoshop (the big-brother to Photoshop Elements), Premiere Pro (big-brother to Premiere Elements), Adobe After Effects (compositing program), and a few more. Again, because of the bundled price, it's like getting 8 programs for the price of 3, but still not inexpensive.
Also, Adobe offers their Creative Cloud subscription, which might be a great way to go.
Just some thoughts, and good luck,