Hi mystery777. The autoresponders that come with most hosting accounts are meant for simple automatic responses associated with an email account that you create. You can also create mailing lists using their autoresponder feature. However, I think that your criteria for an autoresponder will require a seperate solution.
You can try installing something like phplist and run it on your host or simply get a solid autoresponder/newsletter service like aweber ($19.99/mo.) and have all the features you need.
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As for your hosting needs, everyone will have positive and negative experience with any host. The suggestions in this forum have been to the likes of Hostgator and ThirdSphere. One of my accounts is with Hostgator and I haven't had any problems with them.