There will typically be a wine recommendation for the day's menu items. As a rule, if you are unsure, stick with the chef's suggestions.
You can also ask the sommelier - they are usually very happy to help you make a selection in the price range that you indicate. If you prefer not to buy a full bottle, go with wine by the glass. It costs more overall, but if you only having one glass, it makes sense.
Also, I always offer my tablemates a glass when I buy a bottle. In most cases, over the course of the week, it evens out, and everyone has shared their wines as well.
I usually also preorder champagne for my table on formal nights - it is always a nice surprise when people arrive at dinner and find the champagne glasses and we all enjoy a glass or two before dinner.
Don't be intimidated, have what you enjoy. And don't worry to much about the dining room "police". They will be too busy going after the people who aren't dressed properly for dinner