There are many great iOS 3rd party web browsers out there which are nicer than the built in Mobile Safari. However, in Safari, you can add home screen links to pages and you cannot do that in the 3rd party browsers. This is a workaround based on my limited PHP knowledge. It requires that you have a PHP-supported web host and it will only work when you can connect to said web host.
It also requires that your third party browser has some type of link associated registered with the iOS device. My only experience is Atomic Web (atomic://) but I am sure others have it too.
These instructions are not perfect and there may be better ways to do this but it seems to work for me. Read at the bottom for some discussion on the pros and cons of this method.
Some sites (such as Google) have nice home screen icons. If you want them, first, on your computer, use Safari or any other browser where you can change the User Agent and change it to Mobile Safari. Go to the website of interest and view the source. You are looking for something like this.
This may not always be easy to do but I just searched for 'apple-touch-icon-precomposed' and I am usually able to find it. Go to the URL and download the png file. If the site does not have an icon that is 57x57, I think you will have to create one. There may be other ways to do this. If so, please put it in the comments. Also, there are options as to whether or not iOS adds the glare to the icon. Your best bet is to search and read about iOS meta tags.
To create the Home Screen link:
To set up the home screen, first create a file on your site. For example, with a Gmail link, I called the page gmail.php.
I created the page with something along the lines of the following:
<head> <link rel="apple-touch-icon-precomposed" href="gmail-iphone-57x57-p.png" /> <title>Gmail</title> </head>
<?php
header("Location: atomic://https://mail.google.com/mail/mu/#tl/Inbox");
exit();
?>
Mac OS X Hints
http://hints.macworld.com/article.php?story=20110307064851573