SMTP Service.

Hi,
we have a site hosted at one of the providers from whom we purchased the domain name. Unfortunately they dont provide any SMTP service. We are desperate to have a SMTP service as we need a email add’s like myname@mycompany.com. So finally what i wanted to know is i have seen many softwares aroud which has SMTP service, If i buy any softwares which provide that service and install it on any of my server will i be able to send email from myname@mycompany.com????
Can we reach the outer world with our won email address with our domain name??

Please advice.

Regards.