As with all things it sort of depends exactly what you're trying to do. I'm going to imagine that you're trying to send out a weekly email to around 3000 people.
What not to do:
Don't try putting their emails into the bcc field.
It's really easy to mess this up and put it into the cc, meaning that you've sent everyone each others email addresses.
Also doing it that way you end up having to deal with unsubscribes, people changing email address etc. all yourself.
What I'd suggest:
They're both good, I've used both in the past, I have a slight preference for mailchimp as their ceo bought me pudding once but look at both and decide which you prefer.
Use one of their included templates it's free or nearly free, it means that you know it works with their site and has been tested to look good in most mail clients.
After you've sent out a few you might decide that you want to create or have created a specific template. That's great and I'm happy to help with this (by which I mean I can recommend some people), but I'd wait and see if you're happy with what you're doing first and then look at it.
Test, test, test.
Create a small group (3-4 people max) of friendly people who can phrase criticism well (I'm happy to be on this) . Before you send any email out to a large group send it to these people and then email them as a group (this time cc them in) asking for comments. This should mean that some mistakes get caught (some will always get through).
Allow people to unsubscribe easily
This should be covered by the template, the reason you want this is that if you don't do this then people will mark your emails as spam. That means the big providers will start to see all you emails as spam. As well as this mailchimp, campaign monitor or whoever will stop providing services to you (they'll warn you first) they can't afford emails they send to be marked as spam.
Make your emails relevant
Following on from the above, there is no point in sending an email to a group of people that have never been to your venue a discount for those returning for the 25th time. (There are better examples but this was the one that came to mind).
Both Campaign monitor and mailchimp allow you to split your subscribers into groups, do this. It will take time and be frustrating but it's worth doing. It will allow you to send more targeted emails that are more relevant and therefore produce (hopefully) better results. Mail chip also definitely allows you to add code to add subscribers directly from your website, you should do this as well and if you can have them put into specific groups.
Look at the stats
After you've started sending the emails it's important to look at the stats that are generated. It will allow you to start refining what to put in and when you send emails.
That's probably more than enough for a starter and no doubt contains some irrelevant bits that you already know and others that you don't need to.