It sounds like right now you have your own mail server, that you maintain it, and that you are considering the purchase of a second mail server? I'm a little confused since it sounds like you have your own mail server but also mention that you have a basic plan that seems to be provided by a 3rd party.
What operating system (windows, linux, etc), MTA (exchange, sendmail, qmail, etc), and what mailing list software if any (ezmlm, majordomo, etc) are you using?
How and where is the newsletter created? Is it directly tied to the sending or do you create the newsletter on your PC and mail it out based on the smtp server setting in your mail client to the mail server and/or mailing list? Is this a list of recipients in a large address book contact list or an actual mailing list managed on a mail server?
3000 members is a relatively small list that should be able to complete first delivery attempts within a few minutes on most modern mail servers. You certainly should not need a dedicated mail server to handle the load of sending those mailings and processing the bounce messages. Why is the mail server slow? Are you sharing resources with any other domains or mailing lists? Are you reaching the max of a configuration setting for the maximum number of outbound deliveries that are allowed to be attempted in parallel by the mail server? Are the return bounces, out of office messages, and other return traffic generated by the mailing list maxing out the number of incoming connections into the server?
Do you have access to the mail logs? What do they say when the mail server is being slow?
I can't think of a good reason why you should not be able to keep a 3000 member mailing list in house, so I hope this conversation will help us figure out why you are running into slowness problems while sending out your newsletters.