Skiing is a great holiday for people who have nobody to go with - it is a very social activity.
For accommodation, the best option is probably a catered chalet, as you immediately have the other guests to eat, ski and socialise with, but a combination of Covid and Brexit has greatly reduced the number of catered chalets available. Otherwise, a hotel or small B&B/Pension would be good - many hotels have single rooms available at little or no extra cost.
For ease of booking you could book a package holiday with a Tour Operator (Crystal, Inghams etc.) which takes away much of the hassle but which limits your options in terms of departure airports and destinations. Alternatively, if you are confident enough you can book everything yourself. An airport like Salzburg has numerous flights from the UK and there are plenty of resorts within 60-90 minutes of Salzburg, with shared transfer taxis and buses available from the airport. Look at Skyscanner for flights and the resort Tourist Office websites for accommodation, and the usual accommodation sites too (Airbnb, Booking.com etc).
Once in resort you should definitely take lessons. The skis and boots have completely changed since you skied 35 years ago, as has the technique (and of course your own physique will have changed). Book a week of group lessons, which comes with the added advantage of another instant social group of fellow learners who are all at the same level.
Assuming that you're not tied to school terms, stay well away from busy European school holiday weeks (New Year and all of February). January or early March are less crowded and much less expensive.