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This question has various answers depending upon your email list and email marketing requirements. I think that most businesses starting to execute their email marketing efforts will choose an ESP (Email Service Provider). Simply put, there are systems where you can upload your email lists and your creative and send your email campaigns. When using a third party ESP you are really using all their systems and resources. Most ESP's manage their own IP space closely to ensure that there IP addresses stay white-listed so that their client's emails get delivered successfully.
There is a lot to know from a technical perspective so using a third party like the prior thread explains would probably be your best strategy. Again, all this does depend on your business and marketing requirements.
For more experienced organizations where the email list is quite bigger you may want to have the ability to manage your email list management and email marketing efforts inhouse. Having a lot of experience with email marketing systems I can tell you that you want to have your hosting server and MTA (Mail Transfer Agent) on a server that is protected from the outside world. Imagine a bicycle wheel where the hub in the middle of the wheel is your database server and MTA. Each spoke from the hub will connect to a different SMTP server where your sending IP's are binded to the domain names you are using. This model is very effective and will keep your data safe from the outside world. This model is also very scalable and is more sophisticated than the third party ESP example I provided in the beginning of this comment. We have seen the pricing of third party server range anywhere from $100 - $500 per box (server) depending upon how many IP's and how much bandwidth you get on each server.
The cost for email servers and services vary from free to several hundred dollars per month. Nevertheless, there are roughly three different typical price points: the free, the cheap, and the pricey, full-featured ones. Here are some of the vendors that I have used in the past. All of them work with an ordinary Web browser to set up subscribers, format your messages, and manage your mailings. Here's some data from research which is a few months old, for what it's worth...
Free: Google Groups, which has been recently enhanced to work with Google Apps. If you use Google to host your email on your domain (which can be either free or $25/user/year, depending on which of the two plans you get), this is as easy and as cheap as it gets to do email lists. You definitely get what you pay for here, but for small lists it can be a good way to get started. You have to add less than 25 users at a time, but you can add them over multiple steps. (Yahoo is limited to 10 per day.) There are other free providers, including Yahoo Groups and Windows Live Groups, and if you use these for your ordinary Web email needs you might want to take a closer look at them.
Cheap: Mailman, a Linux-based list server that is available from a number of Internet providers. Like Linux, it is character-mode and rock sturdy at sending out thousands of emails at a single shot. For about a dozen years, I have used this to host my own list with the provider EMWD.com for the princely sum of $4/month per list, no matter how big it gets or how often you send out mailings. You might want to check with your domain hosting provider and see if they offer this service for something similar. You use its Web control panel to set up dozens of various obscure parameters once [see screen shot] and then operation is relatively straightforward.
Pricey: ConstantContact.com. This is the Cadillac of email lists, and if you have a large or growing list, you will pay appropriately. They start at $15/month. You can embed trackable HTML links to see who has opened your messages, include pictures, format your messages to look as pretty as you wish, and add custom mail merge fields to make it more personalized. They have a Web control panel that is very easy to navigate to set up new subscribers, choose the graphical template for your list, and schedule when your emails are sent out. They can connect to your Twitter account automatically, and create an archive too for an extra $5 a month.
For what it's worth, I'm using ConstantContact with great success, very easy to use! Nice templates and easy to customize to include my own logo and graphics. If you're trying to maximize your use of time, paying a few more dollars for something that will make your email/newsletter tasks quicker is well worth it.