I realize it's not the same situation, not the same expectations, a different world than 500+ years ago, but real progress doesn't happen in a cleanroom.
The bandwidth back than was more than adequate to handle a website like Hacker News, and the store-and-forward protocols that were developed back then to preserve bandwidth, like SMTP and NNTP, will probably come back into play for a Mars/Earth link. Any video would need to be highly compressed and low quality by today's standards, but in the 50s and 60s TV was far lower quality than it is today and served its purpose just fine. Audio recordings for voice messages likely would be just fine without any quality reduction.
You have to remember that the initial colonists are going to necessarily be a fairly independent bunch. They're not going to need, or care, to keep up with the latest shows, music, or social media. They'll be too busy with surviving, collecting and transmitting scientific data, and writing letters to their loved-ones back on Earth.
But indeed, NASA intends much higher bandwidth for future missions using laser communications.
SpaceX would likely use a variant of their constellation satellites which should be capable of multiple Gbit/s using laser communications.
>Data rates up to 1 Mbit/s
That's a bit of a problem. It only seems to be a relay for other spacecraft and small surface craft. Much more data will need to be exchanged between Earth/Mars when humans are involved (weather, video, entertainment, collected data, software, etc.)
You'd probably want several brand new satellites dedicated to communications for an initial colonial undertaking.