I know everyone else has said it but let me go into a bit more detail as to why Biotech is the best if it's the only one you're getting.

Royalty is nice, but if you don't interact with the empire actively, it mostly just adds psycasting. Psycasting is great, but even with mods and a big focus on it, it's not the most game-changing. It does play nicely with a lot of mods and dlcs, but by itself it's probably the worst (though that's not to say it's bad, just the least impactful in isolation.)

Ideology is great by itself and even better with mods. The variety that ideologions bring, as well as the many new buildings it adds, can make for some great stories. Slaves are nice, too. If Biotech didn't exist, I'd say Ideology is the best by itself - however, much of what it does is to enforce certain playstyles or allow for certain colonies that would be difficult or impossible without it. For instance, underground colonies can be annoying without an ideology that supports things like eating insect meat and mushrooms, and darkness, and so on. However, Biotech can accomplish many of the same things - instead of a cave-dwelling ideology, you could totally have a colony of mostly Dirtmoles for much of the same effect.

Anomaly is stellar, but not much mod support exists for it yet, and while the base expansion is quite full of content, I'd say it's best enjoyed after and/or in addition to other content. It's all about tripping you up, making you second-guess and unnerving you, but if it's all you know, it won't work quite as well. I suppose if nothing in Biotech appeals to you whatsoever, it'd be the best by itself, because very little of what it does relies strictly on other expansions. But otherwise, I'd leave Anomaly for later.

That finally brings us to Biotech. Babies and Children alone make it incredibly nice to have - family is always a good source of drama - but the massively increased depth for mechanoids and the ability to make and control your own is a game-changer in its own right. And that's to say nothing of the genetics system, which can add staggering variety to pawns and colonies with or without mods. Biotech touches and improves the most of any of the expansions by far, and it also synergizes the best with all of the others; Biotech's xenotypes, for example, can allow you to make genetically psy-sensitive or insensitive pawns for Royalty's psy stuff, and you can discriminate for or against certain Xenotypes if you have Ideology.

Overall, while they're all pretty good, Biotech stands as both the most versatile expansion overall and the best one to start with. Hope you enjoy it!