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Now, you said this can be done through our "regular mail client". What is that?
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Your regular email client is Microsoft Outlook, Eudora, Mozilla Thunderbird, ... whatever product you use to send and receive emails.
If the mail-out is going to be one time, you could just copy-and-paste addresses from the Excel document to the email client and send out the email that way.
The number of emails you can send out is usually specified by your ISP (Internet Service Provider). Some companies restrict outgoing emails to 500 per day, 1000 per day, or some other number. You would have to find out what your limit is if you want to consider this option further.
CMS is Customer Management Software, like Salesforce. This is the product that companies use to contain all the information about their customers, for example, contact names, titles, addresses, email addresses, telephone numbers, etc.--any information you want to retain on your customers. If you are already using saleforce.com, you should be able to add all the customer information into saleforce, and do the mail out from there.