Allow User To Generate A Blog Post

You can do that with roles assigned in admin. However the Role Manager plugin lets you be more flexible with your roles.
http://redalt.com/Resources/Plugins/Role+Manager

I don’t understand, do you want them to make a blog post that will appear on the very front of your site?
Or do you want them to make comments to your blog posts, that appear under the blog post on the page for that post?

Comments is easy, go to Dashboard > Options > Discussion and make sure “Anyone can post a comment” is ticked. So that you can moderate them first, make sure “Hold comment” is ticked.

Blog posts I have no idea.