How to make changes to default theme


I like the default theme but would like to make some changes to it, if they are relatively easy to do.

1) I'd like to replace the blue logo bar with a tiling background.

2) I have my site set so that a visitor can only see the index page unless they are logged in.  However, I really need the index page to be jazzed up a bit.  Is this a job for a theme, or is this something I have a lot of manual control over?