Resizing the website inside the app page is easy in the app settings. But the thing you need to consider upfront is this:
Facebook Fan Pages only accept 520px wide iframes, so your website needs to be variable width and use some shrinking code before you put it on that page - or even better, design your page so that it's 520 pixels wide. There's definitely no room for a sidebar. Trust me, the APP page is useless, and nobody wants to visit. Also, you need to try to avoid having Facebook curse you as a 'Community' page. I think this means you need to sell something, otherwise you cannot set your default tab to be your website. This means users will arrive at your built-into-facebook website and face the YAWN, Wall tab first. There's no clear way to tell them to press the tiny button under Your logo, Wall Tab and Info Tab on the left so that your web page appears.
Make your website 520 pixels wide so that you can put it on your FAN PAGE (as app pages are neve visited),
and avoid being cursed as a Community page by Facebook.
Take a look at the link I made in the top left of www.theatrenetwork.com.au
. It's a button I invented called 'View this website on Facebook'. It's the best I could think of to make use of having an unfindable app page.
See some of my previous threads for instructions on how to create an overall_banner.html file. Removing the solid colour behind my logo so the background image shows through has transformed my site's aesthetics markedly.