Some games before others?

Well, the games tend to have a lot of stuff spread off through different games, which allows for some calls no matter which game do you decide to start with.

:OoT: and Majora's Mask are probably the most obvious sequel games showing beyond a doubt the same protagonist so playing OoT help you explain things further, however, what we miss if we don't play OoT are only the nods to that game so a person can enjoy MM without having to play OoT to make sense of it.

Quote from Silent Lion

the intro and outro would make no sense,

It makes enough sense in the sense that it is the same zone where we see him start the journey so he got back to that point safely. The drawing on the log by MM context could had been the skull kid, just like he did in Termina. Through ooT we know the possible name of the zone and the friend we don't get to see.

Quote from Silent Lion

the ocarina and Goddess of Time would make no sense

The Ocarina is explained by a flashback. OoT only expands more on why Zelda holds it and why it has mystical powers.
regardless teh Goddess of Time, ooT doesn't really provide any concise information, really. I think only MM makes allusion of that name.

Quote from Silent Lion

you wouldn't really know what a skull kid was meant to be

But that is not something you need to know to emphasise with the skull kid in this tale.
I actually think it is just as satisfying playing ooT second and discover one by one the references from MM. Finding how Link met Epona, doing the mask exchange quests with the skull kid, finding the familiar faces and slowly understanding that the text at the begining of MM is relating what you're living through right now would be as exciting for a gamer.

I started with Ocarina of Time, so imagine my surprise to find the Sage name's being provinces for 'Adventure of Link'. For people that played AoL, OoT was the throwback moment, for either the idea that the sages were immortalised through provinces was understood regardless the order. Then with AlttP checking the three pendants, sword, Sages, the Kakariko music and the Lost Woods area. The more games you paly the more things you start to piece together.

So, I don't think it is a must to play any other game but I think that playing more games expands the lore and meaning of some elements you passed through other games, enriching the experience and making you feel more connected with that world.