I went through all this a while ago. I checked out a few of the stand alone applications (like mailloop) that run on your computer, and i looked into both aweber and getresponse. To be honest, for the money i'd recommend going with getresponse. It's really cheap (about $18 a month), and they automatically handle subscribing + unsubscribing members, handle all bouncebacks (bad email addresses), and ensure that your list is whitelisted. They've got a lot of other features that i'm forgetting - but i think it'd be worth it for you to sign up for their services + import your existing list
I really like using and highly recommend Simple Mailing List. It's easy to use, fast, quick, clean interface and totally free. You can get it at: www.notonebit.com/projects/mailinglist/
PHP List Manager is a good program and free. You have to have a host for it. You can check it out here: www.phplist.com