Skating is easier than classic to get to an intermediate level where you can move along pretty fast and have fun. Classic skiing will only a little bit more specific to alpinism and ski touring. But the training transfer to hiking/climbing uphill in the mountains from either classic or skating will be very high so should not be your main consideration in determining which technique to pursue. Is sounds like you live in a coastal region which means more frequent temps close to freezing. This means more difficult kick waxing on classic skis although alternatives now exist such as “skin” skis with use a short mohair strip in the kick zone of the classic skis and several companies make this available on their higher end (but not top end) skis. This is typically a better choice than fish scale waxless skis. Skating skis will easy because you don’t have to deal with kick wax at all. Just jump on them and go.
Get lessons if yo have not skied before. They will speed up your learning curve appreciably.