I'm assuming you are using Linux or Unix. My take is that any of Sendmail, Exim or Postfix are fine as MTAs and as a starting point would consider whichever is a default on your OS or distro, as it's more likely to have a good basic setup out of the box. I've used all 3 at various times. My perception is that as any of these MTAs is more than sufficiently performant for common use cases, the complexity of configuration is a big deciding factor if you are considering choosing a non-default MTA for your OS.
Sendmail, the oldest widely-used MTA, has a notoriously opaque low-level config file, though there are some higher level abstractions available; I therefore rank Sendmail as worst for configuration complexity. When Postfix was supplied with a new (to us) OS version some years ago, I rather fell in love with the comparative simplicity and power of its configuration and so now use Postfix personally, whenever I have a choice. Exim has an intermediate level of difficulty.
So what about MIME::Lite and its use of "sendmail". Well, it so happens that both Exim and Postfix come with a "sendmail" command as standard, which mimics at least the core functionality of Sendmail's CLI. MIME::Lite looks in /usr/bin/sendmail, /usr/sbin/sendmail and then for a sendmail command in your PATH. So it's likely to work just fine with any of these MTAs without any work. I'll leave the question (also mentioned by 1nickt) of whether to use MIME::Lite given the statement these days in its documentation that it's no longer recommended (though I have used it without problem in years gone by).