[exim] Help for exim configuration

Hi All,

I'm trying to setup exim to a linux server(ubuntu), this linux server is located in my company's network.  I use below command to change the configuration: 
dpkg-reconfigure exim4-config
On the first page the configuration, there are several choices: 
(1) Internet site; mail is sent and received directly using SMTP. If your
     needs don't fit neatly into any category, you probably want to start
     with this one and then edit the config file by hand.

 (2) Internet site using smarthost: You receive Internet mail on this 
     machine, either directly by SMTP or by running a utility such as 
     fetchmail. Outgoing mail is sent using a smarthost. optionally with
     addresses rewritten. This is probably what you want for a dialup
     system.

 (3) Satellite system: All mail is sent to another machine, called a "smart 
     host" for delivery. root and postmaster mail is delivered according 
     to /etc/aliases. No mail is received locally.

 (4) Local delivery only: You are not on a network.  Mail for local users 
     is delivered.

 (5) No configuration: No configuration will be done now; your mail system 
     will be broken and should not be used. You must then do the 
     configuration yourself later or run this script, /usr/sbin/eximconfig, 
     as root. Look in /usr/share/doc/exim/example.conf.gz

The first time, I choose option 1, however, using this configuration, I'm able to send email to my company email address, when sending email to outside email address such as hotmail, it will report timeout error. And when I use my company outlook account to send email to this linux server, it never get this email.

Then, I change to use smart host (option 2) and I specify our company's smtp host , then I'm able to send email to both internal mail address and external email address such as hotmail. However, I'm still unable to receive email when I try to send email via my outlook , I don't know how to configure exim to have it work? And from technique point of view, I'm confused on the concept for SMTP relay, I could configure my linux server's exim for SMTP relay, however, how does my company's SMTP host know that there is a SMTP configured in my linux server and start relay email to my linux server?

I'm newbie to email concept and exim, really appreciate for any of help from you. Thanks a lot in advance!

Regards,
Qi