Cross-country skiing vs alpine skiing: which one should I choose to start with?

It really depends on what appeals to you more, to be honest. Alpine skiing is more adrenaline-fueled and faster, but it demands more leg strength at the start and falls can be more traumatic. Cross-country is calmer, less physically demanding if you're not trained, and you learn the basics of skiing technique without the stress. If you just want to learn and enjoy the mountains, start with cross-country, then you can always switch to alpine later. You've got excellent instructors in Livigno anyway, so you can't really go wrong.

I mainly work with audio, but my dad tried both when we were younger and he always says alpine skiing is easier for beginners because you learn speed control and braking pretty quickly, whereas with cross-country skiing you need to already have some coordination. At Livigno you've got beautiful slopes for alpine skiing anyway, and maybe after your first lessons, if you really like it, you can try cross-country skiing which is more "chill" and romantic, perfect for long outings.

Cross-country skiing burns about 600-700 calories an hour while alpine skiing uses 400-500, so if you're in decent shape cross-country might put less pressure on your joints at first. As a paramedic I see skiing injuries pretty often, and I can tell you beginners on alpine tend to get hurt when they lose control going downhill, while cross-country is more forgiving because you're going slower and on flatter terrain. I've seen quite a few friends who started cross-country in late summer doing long hikes, and by the time they put skis on in winter they already had the right endurance without that fear of falling off a cliff that freezes a lot of people up their first time on alpine. If Livigno has easy runs for alpine maybe it's still worth a couple of lessons, but if you really don't know where to start cross-country is less traumatic both physically and mentally.

First try to figure out where you want to end up, not where you're starting from. Let me explain: if your goal is to do relaxed mountain hikes maybe with friends, cross-country skiing is perfect. But if you want to go off-piste and have fun doing some fast turns, then alpine skiing is what you need to do. It's not that one is easier than the other for beginners, it's just a completely different thing.

The real detail that nobody's told you: in Livigno you'll have different slopes and terrain depending on what you choose. They teach you alpine skiing directly on the ski slopes, with the lifts, meaning in the real situation where you'll actually use it. Cross-country skiing on the other hand is often learned in flatter, more controlled areas, which is nice for learning the technique but then the transition to real practice is different. If you really want to ski right away, alpine puts you straight into the actual context.

Also consider that the equipment is pretty different, and if you change your mind halfway through winter you can't really use one type of equipment for the other. I'd say try both maybe in two separate lessons, if your budget allows it, and figure out right away which one you like better. After the first lesson you already know if it's your thing or not.