I suggest looking at Frwiki's main page. They overhauled it a couple of years ago, and it's responsive, and I believe (but not sure) it has been checked for accessibility. Here are the links I can find, but I'll ping @Trizek-WMF in case he knows of further links.
https://fr.wikipedia.org/wiki/Wikip%C3%A9dia:Accueil_principal
https://fr.wikipedia.org/wiki/Wikip%C3%A9dia:Refonte_de_2017_de_l%27Accueil_principal_(FAQ)

In T241646#5790742, @Quiddity wrote:

I suggest looking at Frwiki's main page.

Thanks Quiddity!
Looking at https://fr.wikipedia.org/w/index.php?title=Wikipédia:Accueil_principal&action=edit with its boxes, and its related CSS defined in https://fr.wikipedia.org/w/index.php?title=MediaWiki:Common.css (search for accueil) it looks like they use a flexbox design.

For T653 a year I also ended up using flex for the boxes on the mediawiki.org frontpage, see the CSS in https://www.mediawiki.org/w/index.php?title=Template%3AMain_page%2Fstyles.css&type=revision&diff=3175861&oldid=3151579

For browser compatibility, see https://caniuse.com/#feat=flexbox
For general info, see https://developer.mozilla.org/en-US/docs/Web/CSS/CSS_Flexible_Box_Layout/Basic_Concepts_of_Flexbox

For the records, for T653 I initially also looked at grids ( https://caniuse.com/#feat=css-grid ) and don't remember why I decided against it. Not a web designer.

"Templates" part moved into dedicated T246180: Small Wiki Toolkits: How-to guidelines and/or potential recommendations for Templates hence edited task summary / desc.

• Should cover / keep T32405 in mind which is not always known. See T174406#3567413 for such an example.
• Might welcome input from Reading Web, pages exist such as https://www.mediawiki.org/wiki/Reading/Web/Projects/Mobile_Page_Issues

These two my items are about mobile though. Right now I don't see how they are problems, as folks would end up with MobileFrontend / Minerva rendering anyway.

Aight, Init draft at https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 in kind-of simple language. Feedback welcome.
TODOs:

• Who gets interfaceadmin rights when a new wiki is created? If nobody, then how could/would I change my main page?
• How to disappoincommunicate feedback / support expectations? We're not a generic CSS/HTML support place. Link to Stackoverflow? :P

@Aklapper Looks good! I've a few comments/questions:

• For the line "Copy and paste these CSS definitions into the page MediaWiki:Common.css. Make sure that you use specific names (names in the example....", I think it will be helpful to re-iterate that only interface admins will be able to make this change. Also, make it clear what "specific names" here means. Perhaps, they should be rephrased as "unique names"? Maybe also in the example here https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Define_the_CSS, you could use more unique names so that there are almost no chances of that CSS getting applied to other pages as a result of copy and paste.
• Maybe there should be a note here https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Further_information on how the TemplateStyles approach is different from adding to Common.css
• Also, maybe in the example section https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Example, it should be made clear if/when CSS should be added to Common.css and for which pages, main page, all the pages, etc. Is there an alternative? Newbie question - can something be added to the wiki page itself for responsiveness?
• Lastly, I'm wondering if https://wikitech.wikimedia.org/wiki/Wikimedia_site_requests & https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 should all be on one page itself, as they are related topics. May be you have a plan for this :)

• Incorporated feedback by MF-Warburg in https://www.mediawiki.org/w/index.php?title=User%3AAKlapper_%28WMF%29%2FSandbox%2FT241646&type=revision&diff=3717187&oldid=3692715

In T241646#5962178, @srishakatux wrote:

@Aklapper Looks good! I've a few comments/questions:

• For the line "Copy and paste these CSS definitions into the page MediaWiki:Common.css. Make sure that you use specific names (names in the example....", I think it will be helpful to re-iterate that only interface admins will be able to make this change. Also, make it clear what "specific names" here means. Perhaps, they should be rephrased as "unique names"?

Done.

• Maybe also in the example here https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Define_the_CSS, you could use more unique names so that there are almost no chances of that CSS getting applied to other pages as a result of copy and paste.

Replaced mainpage with wikifrontpage. Don't think I can get more specific. :)

• Maybe there should be a note here https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Further_information on how the TemplateStyles approach is different from adding to Common.css

Added an explicit See [[mw:Special:MyLanguage/Help:TemplateStyles|TemplateStyles]] for more information. as I don't want to duplicate documentation.

• Also, maybe in the example section https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#Example, it should be made clear if/when CSS should be added to Common.css and for which pages, main page, all the pages, etc.

Added the sentence The CSS in [[MediaWiki:Common.css]] affects everyone and is executed automatically for both logged-out and logged-in users.

• Is there an alternative?

There is an alternative via TemplateStyles, covered below.

• Newbie question - can something be added to the wiki page itself for responsiveness?

I was torn on that one, as I cannot centralize the CSS within the page and did not want to put it inline as <element style="x, y, z">. However you have a point, so I added that to the beginning. See https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646#What_you_can_learn_on_this_page

• Lastly, I'm wondering if https://wikitech.wikimedia.org/wiki/Wikimedia_site_requests & https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 should all be on one page itself, as they are related topics. May be you have a plan for this :)

I don't think it should be. One requires Gerrit, the other one does not.

Only thing left in this task is finding a good location where to move this page. And then link somehow from https://meta.wikimedia.org/wiki/Small_wiki_toolkits

...and I finally realize that we really must rework https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 and cover TemplateStyles.
TemplateStyles are the way to go. See T228604 or T248416 for more references.

Alright, I rewrote https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 to use TemplateStyles only and not (ab)use MediaWiki:Common.css.
Review welcome.

In T241646#6027722, @Aklapper wrote:

Alright, I rewrote https://www.mediawiki.org/wiki/User:AKlapper_(WMF)/Sandbox/T241646 to use TemplateStyles only and not (ab)use MediaWiki:Common.css.
Review welcome.

I think the paragraph about interfaceadmin rights can be removed now that it is not using common.css. I could be wrong about that though. Various wikis will have applied some sort of edit restrictions to their Main_Page (or local language equivalent), but I don't know that there is wiki-farm wide default for the group that is granted the edit rights is. For enwiki (never the best example) the group needed is sysop via transclusion in https://en.wikipedia.org/wiki/Wikipedia:Cascade-protected_items.

I made a few edits to use <syntaxhighlight/> to add some color to the code blocks. I also added a footnote providing a bit more information on why common.css is not a great way to layout Main_Page. Things felt pretty readable and understandable to me after all your work, but I'm probably a better technical reviewer than a clarity reviewer.

@bd808: Yeah I only kept interfaceadmin in there because of the Main_Page. Thanks for your edits, appreciated!