I've been researching Aweber so I know how the system works inside out. Here's a few things I've tested with follow ups that might save you time instead of having to do your own tests to find out yourself.
Aweber have autoresponders called Follow Ups
You can have a follow up after subscribing to a mailing list.
You can set the days after the initial subscribe that the follow up/autoresponder will be sent
You can set multiple emails to be sent on the same day. Day 0 = immediately after subscription.
You can attach files to your follow up email (very cool)
You can add follow ups anytime and they will be delivered. So say you want to add a new follow up for the 2nd day after signup. You might have members who have been subscribed for a month already. When you add that new follow up, anyone who has been a member for longer, will get the email immediately (this might or might not be a problem depending on your point of view)
On a personal note, I think the Aweber email system is the best one I have seen online. It doesn't try to do everything. It provides a tool for email marketing and list management, and does that VERY well.