Edit II: The Edit Wars - I've just read what SimpleNews provides and see that it is a newsletter sender. Skip the next edit and go straight onto the last block.
Edit: The Phantom Edit - My answer is in the understanding that by mailing list, you meant newsletter. I see now that you could just mean a forum-by-email (like many open source projects operate, for example).
If it's the second, you're probably fine just sending it yourself. Sending a couple of dozen emails to each user at once isn't going to kill your box and hopefully won't get you labelled as a spammer.
If it's the first and you're sending 1500 emails at once for marketing interest, read on.
I would always argue for a third party service for mailing list - especially if your make money from people actioning these emails.
Why? Because it's so easy to get blocked as a spammer (even for legitimate emails) if you send enough email. By using a third party, it's their job to deal with making sure your IP (with them) remain's unblocked and trusted by all the major players in the spam-scanning world.
It certainly costs more than doing it yourself but with a lowish volume like 1.5k/month, you're probably not looking at that much money.
I use iContact for a client and they've been just great. They have fairly detailed reporting as well (so do lots of email companies) which their marketing bods love. Would cost you $25/month for your volumes.