Starting from the outside in.
Active Directory will need Dynamic DNS of some kind. If your existing DNS servers can't do that, then you'll need to use different DNS servers for just the AD domain itself. This is actually a pretty common config. The DNS domain used by Active Directory is something else than where you receive your mail (example: if you're at example.com, set up your AD to run in internal.example.com). All other DNS remains as is.
You want to keep the MX record for your external domain (example.com) pointing at your existing mailer. That doesn't change. It's the config on your existing mailer that'll have to change.
Depending on what's running on that existing mailer, you will have to configure it to forward all mail destined for your domain to your Exchange system. This is a pretty common config as well, as many anti-virus/anti-spam appliances require this kind of setup. It's pretty simple to set up in most smart mailers.
Setting up Exchange: mail domains
Once you get Exchange installed, you've set up your mail box databases and suchlike, it's time to set up the policies that determine the email addresses that get passed out. In Exchange Console, go to Organization Config -> Hub Transport -> Accepted Domains tab. Make sure that your doman is in this list, and set to default. Then on the E-mail Addresses tab for Hub Transport, right click on Default Policy and go to Edit. Following this wizard will let you set up what email addresses Exchange assigns to users by default. This is where the choice of email@example.com vs firstname.lastname@example.org gets made.
Setting up Exchange: outbound routing
You didn't specify if you wanted all outbound email to be sent via your existing mailer. Just in case, this is how you'd set that up. Under Organization Config -> Hub Transport will be a tab for "Send Connectors". One of those policies will have "to internet" in it (I don't know what the policies look like on SBS so I can't be certain what it is). Go to Properties on that, then the Network tab. Click the radio button for "Route mail through the following smart hosts", and enter the address info for your existing mailer.
This will set up Exchange to it uses your external address for all email, internal and external. It's simpler this way, and is a very, very common config.