The number one factor when you are considering purchasing your own skis is to try before you buy where possible. Skis are expensive, and once a ski has been used on snow, impossible to return. Review websites such as Ski-Review.com can be useful to assess an overall perspective, but be aware that all skiers are different and therefore a positive or negative experience will apply to that reviewer and that reviewer alone. Take a general consensus and always factor in the skiers skill, ski length, weight and height.
Most ski shops should be able to arrange a demo using their own stock or rental skis - therefore it is a good idea to do this on site so-to-speak i.e. arrange a demo from a stockist in resort.
Please see below a brief checklist of the fundamentals you should consider when buying skis.
Gender
Men and women are physically different and therefore there are an increasing number of women specific models available. Jeannie Thoren has spent a number of years researching the way women ski - well worth a read - http://www.jeanniethoren.com/
Skill
Not all skis are born equal, therefore within each skiing discipline (see below) there will be a range of choices intended to match your skill. As with most skills, your equipment should be able to cope as your ability level increases, therefore you should buy a ski intended at a level slightly higher than where you ski currently.
Discipline
Consideration of the type of skiing you enjoy and intend to use your new purchase for is important. Freestyle, Recreational, All-Mountain, Piste Carving? In all probability, if you are unaware if this yourself you are likely to want to stick with a ski in the recreational category. If your skill level is considerable, then you should know what type of ski you require.
Ski Length
Length is extremely important in modern design. Too long or too short and even the most suitable ski model for you becomes a nightmare. Skill progression is an important aspect to consider as beginners will generally start using shorter skis (easier to turn, less ski to handle, slower in a straight line) and move up to longer skis as skill and confidence increases. Trained individuals in ski stores will be able to advise a suitable length, and do not be offended if you are asked for your weight, as both your height and weight will influence the length of ski suitable.