How do I run a url shortening service, and monetize it?

I've often come across posts on the internet discussion what URL shortening service works best (many in this forum). Most of those discussions are from the perspective of someone who is using the service. Stability, tracking, reporting, customization - those are all variables in the mix.

However, I'm thinking of it from the other side. For some reason it struck me today that it would be cool to have a URL shortening service. I know there are many ways and suggestions for shortening/cloaking your own links (eg. pretty link plugin or any number of other self-hosted solutions), but I wonder how to provide a service available to all internet users. Mainly, the motivation is one of taking advantage of everyone's need for internet "plumbing" (eg. hosting, domains, email, etc)

I googled "URL shortening scripts" found out that there are many, many options. One of the first articles I came across was this one: 10 Free Scripts to Create Your Own Url Shortening Service. I thought it was useful (though almost 2 yrs old by now) and you might enjoy it too.

I have several questions I'm hoping this group could help me with ...

1. From a perspective of establishing my own url shortening service, what script do you like the best?
What are the pros/cons I should look at?
free vs paid?
what features matter or don't matter?

and

2. How can I make money off of it?
Assuming my intention is to make a profit, what are some suggestions? There is always adsense, but that feels so untargeted because I can't imagine how I would know what people are looking for when they come to shorten a url.
So, i know budurl charges. But for anything short of a paid subscription, how are any of the others making money (if they are?).

3. What is SEO impact?
is there any way to take advantage of all these links to my domain name (which would then be redirected?)

Thanks in advance for your thoughts :-)