For web design, I believe that either Elements or full version of photoshop will work just fine. Elements will do more hand holding with wizards, etc. but its larger brother has more power without any hand holding. Meaning it may take a few more steps, but normally can do more as a trade off.
What neither one can do is svg graphics, that would require illustrator and/or edge animate. (Normally graphics are created in illustrator then animated in edge)