A good welcome series positions and introduces prospects to your brand. If you run aggressive acquisition campaigns to grow your list this positioning takes priority. Newly acquired external leads (e.g. leads acquired via EDM list rental campaigns, promotions etc) will not be familiar with what your brand represents and what products/services it provides.
This is why the start of a welcome series should be used to build position, credibility and trust prior to presenting stronger sales messages.
For me the primary goal of a welcome series is still financial. I want to recover the acquisition cost of new leads using the series before funneling them to receive regular EDMs. If you can deploy a welcome series that recovers this cost you can begin to grow your subscriber base at scale.
A good welcome series should be reviewed and improved regularly. If you ran a strong one-off revenue generating EDM to your subscribers why not add this as an email at the end of your welcome. I love the idea of a long welcome series filled with proven emails.
Finally, test, test, test. Every email in a series should be tested at all times. Personalisation (is using firstname better than title lastname), copy , frequency etc. Like training for a running event improve results in small gradual increments.