Painless way to import content from old custom CMS
"Painless" data migration? You're kidding, right? :)

There are numerous answers suggesting the Migrate module. It is certainliy an option, but one I've never liked. I've done dozens of projects with migrations of content from external systems into Drupal (sometimes from multiple external sources simulteneously), including projects with millions of pieces of content, and I'll argue 'til my death that a Batch API implementation in a custom module is the way to go. 

No two migrations are the same. Each individual migration will involve 'proprietary' cleanup, data sanitization/changes, etc. The only way to have total control is with an entirely custom script. Don't settle for an easy "80% of the way there" via a generic tool and then struggle for weeks as you bash yourself against that 20% that the tool doesn't handle. 

Do it custom, use Entity Metadata Wrappers, and track legacy &lt;--> new content ids in a separate db table.

It may also be an option to simply 'dump' the existing content, markup and all, into a 'legacy' content type and call it a day without moving things into fields and complicating your life. You should sit down with the client and figure out exactly what they want/need, and what they're willing to settle for. Sometimes a simple solution that is just "okay" is a heck of a lot better than the multi-month project that's "awesome."