First off, I think this stuff promotes itself, and has been doing so since GNU of 1984, not to mention the explosive singularity of Linux proper in the early 90's. Today, more and more games are working on Linux, with even a few native offerings.
Steve Ballmer once said, and I paraphrase with Chief Wigham: "Linux is the cancer. Linux is the cancer, and we are the... (what cures cancer?)" Now Microsoft has written GPL'd kernel code, and there's barely a forum out there where someone hasn't mentioned Linux. Not just techie forums, either. This stuff is viral (although it seems slow!)
There's been a lot of UEFI secure-boot stuff been going around, and all I could think was someone pulling an antitrust and some court making Microsoft put Ubuntu, FreeBSD, Linux Mint, Reactos etc on their installation screen as an "OS Choice" thing. I'd rather people found out about Linux under friendlier terms...
I've written whole essays to Windows users on how to run and care for their PC's, and between Disk Cleanup, registry cleaning, defragging - not to mention security scans - frankly, it's ridiculous. Setting up a new PC from empty silicon to workstation can take days. With Linux, especially Mint, half an hour, tops. That's it's main selling point to me.
For Mint in general, I get the feeling it's not a fan club, like Ubuntu, but a community, where the developers hang out with the noobs (unlike Debian, which is cool because that's them!) and actually listen. I think that's been the selling point of Mint, and why it's rocketed in popularity. The upshot of that is it's actually efficient and beautiful to look at, too.
Still, if you have the need to proseletyse, here's what I recommend. Feel free to tear to shreds, that's science for ya!
1. An official banners page on Linux Mint website - either commissioned, or community competition-sourced, centrally approved as official. Cut and paste code for your website, or in case anyone has any freebie AdWords (Google sometimes gives me some...)
2. Leaflets. "Free your PC - In Style" sort of things. Why choose Linux, why choose Mint, quotes from the community about how great a community it is (and I think Mint has one of the best!) and downloadable as PDF. There could be different versions, for home users, businesses, OEM's, etc.
3. Package design. I know a software box is cliche, but still makes it look all official. Windows and Photoshop have nice ones in my opinion. Red Hat and Ubuntu come across as desperate, like they have too much to say. Mint branding should be cool and dramatically simple. Also PDF's. Could include a Jewel Case booklet (with the first couple of chapters of the guide) and a backing sticker.
4. A real-life paid for version, with box, book etc. Maybe a limited edition every LTS with complementary mints (idea credited to Wacom!), poster, pendrive etc... Punt it to all the shops, from Tesco to Amazon. I remember being blown away to see Suse in PC World on the same rack as XP a few years ago. Think what Mint has to offer the casual home-builder today!
5. A Youtube channel with an official "What is Linux Mint" presentation, followed by adverts for all upcoming releases. Interviews with developers, howto's, general highlights from Linux, GNU and open source...
6. Individual promotions. "Test-drive Maya and win a Mintbox!" Bit of an expense, but worth it, especially if you made a review or survey part of the requirements. Could tie in with limited editions.
Apart from that, I like to run Mint at home, and let people use it. Desktop effects are (perhaps sadly) what makes most people go "Wow!" Also, showing somebody how you install software can really make their head turn. For my counterculture friends, I advocate the freedom and pleasure of "sticking it to M$" and all that jazz. For techie friends, including gamers, I show them how you can add stripping down the windowmaker and OS to all the other stuff they do (like overclocking, extreme cooling, etc). For games that don't work, there's dual-booting... Non-techie people come to me for laptop cleaning, and I offer to dual-boot when I'm done. For most of them, whatever gets them to Facebook and Youtube with the minimum of fuss is what they prefer. The Chromebook campaign is a perfect example of targeting to that market.
That's what I think, anyway...