Grand Companies only had really specific benefits between each one in terms of gear back in the original version of FFXIV (version 1.0), however that has long since changed with ARR (hence that article presumably used this now outdated information and treated it as if it was still current) - now GC gear pretty much only differs appearance wise (stats are pretty much the same across all three GCs). So go with whichever you like the look of/lore wise the most!

As for being able to change, you can change your Grand Company once you have reached the current maximum rank with your current one (Second Lieutenant), and then speak to a npc at that GC HQ to change. It costs a fair amount of company seals though, and it should go without saying when you change over to the new company you will start at the bottom again. Thankfully though your previous ranks remain in your old GC so if you switch back it will be as if you never left rank-wise.