By watching all of these videos and practicing a bit on my own, do you believe I will gain the appropriate knowledge base to create a solid web application?

I do not see why not if you are motivated enough. I would even pursue 'social coding' on Github. Seek a project out and see if you can contribute? Learn from others after you have the basics down so you can ask constructive questions and hone some skills. Could serve as a mentor of sorts that you are seeking.

Sounds good, will look into and pursue it. Thanks!

Give http://codeschool.com or http://teamtreehouse.com a try. They should put you well on your way.

Thanks a lot, codeschool seems quite useful!