Sweet or dry?
Like wine, residual fruit sugars will hugely affect the final taste, and there is a scale of bitterness on top. A dry cider (no added sugar) may make your cheeks pucker if made with bittersweet apples, high in tannins and acidity.
Cloudy or clear?
Depends on the apples and their pectins. Traditional ciders will be dry and cloudy due to an absence of sugar, which some makers use to clarify the liquid.
Still or sparkling?
Cider is still unless dosed with sugar at its second fermentation. The process of keeving (more popular in France) creates fizz with no extra ingredients: the pulp of very tannic apples is macerated for 24 hours prior to a slow fermentation.
Any old apples?
Pretty much: virtually any strain will make cider. Bona fide cider apples are bittersweet (with great names like Foxwhelps) but are not worth eating. West Country makers use them most. Elsewhere, combinations are often used.