You broadly have three choices when it comes to skiing - a self-catered apartment, a chalet, or a hotel. Each has its own advocates, and its own attractions. Do check the location carefully to try and gauge whether it's an easy walk to the slopes, lift or bus, and if you can ski to the door or away from it, is the slope suitable for a beginner?

Chalet
Think of your chalet the same way as you would a normal holiday rental, but with a lot of wood inside and out. The main differences are that for many you don't have to take the whole thing - just a room, or two if you need it for family. Others, especially in peak times, are taken as a whole. Most chalets are between four and six bedrooms but there are those that can sleep any number between two and 50.
The next option is whether you take it (or it is offered) catered or uncatered. The latter speaks for itself, but the catered option throws up a series of further options. These range, with appropriate (hopefully) price differentials, from not-very-good young chalet 'hosts' who can sling together a spag bol and a chicken stew, to five-course blowouts with wines included. Meals are generally taken together, perhaps with an earlier sitting if there are kids. It's normal to also include breakfasts and afternoon tea in these packages, and for the staff to have one night off per week - either fend for yourself, or book a restaurant (they tend to all have the same night off, leaving a rush to grab a table).
Amenities you might find as you climb the price scale include mid-week bedding change, a games room, steam room, boot dryers,Jacuzzi, pool, childcare, and ski guiding - which is basically showing you the slopes - and concierge and chauffeuring services.

Apartment
Normally the least expensive option, but more luxurious properties that offer spacious accommodation and perhaps a shared pool, and a balcony overlooking the slopes, will not come cheap. Do study floorplans and descriptions carefully; some properties (France has a bit of a reputation for this) can be small. Most resorts have a supermarket that will see you through a week quite happily, and practicalities like washing baselayers or making a packed lunch are obviously going to be less hassle than in a hotel.

Hotels
Just as with hotels anywhere else, there are tightly defined seasons and wildly varying prices - more than double is perfectly common - between high and low. The ski season lasts between Christmas and Easter so hoteliers are very keen to maximise their yields at the peak periods - this means finding a hotel, in Europe at any rate, which does not tie you in to a half-board deal is rare. For the same reason, booking less than a week is often difficult at peak times.
Hotels are often good places to help with some basics like getting your ski pass (they get a small commission) and they may have a link to a ski school or hire shop (but SkiBeginners get up to 40% off with SkiSet anyway). When we travel with kids we like to try and get a hotel with a pool for when bad weather hits; having a sauna or whirlpool is a nice extra too.
You'll want to stoke up on breakfast for a big day on the mountains, and no-one bats an eyelid if you come down in your ski pants, fleece and socks unless you're at a very formal hotel indeed - in which case wear their little slippers they hand out.
In the evening, many hotels have understood the strange British custom of feeding younger children early and then getting them off to bed or a movie. Be aware though that child discounts will normally only apply to kids sharing rooms - very few will discount if they take a room on their own. Most hotels will offer a locker for your skis, poles and boots, and many forbid this gear in the room.