The specialized Allez is a good starter bike and you can pick up some great bargains this time of year. With your budget I'd say you are better off looking at second hand bikes as you will get a better bike for your money. I'm guessing from your post you are pretty new to all this I've stuff so I would take someone along who knows about bikes to help you check it all out if you do go used.
The best advice regarding bike is get a good frame and make sure it fits you. Different brands have different sizing so do a bit of research into sizing of the particular bike you want/have seen. It may also be a good idea to go into a few bike shops and sit on a few, get some advice re: sizing.
Double/triple refers to the number of chainrings at the front, where the cranks and pedals attach to. Most people use a double but a triple will make hills a little easier as gives you a wider range of gears. You can also get a compact, which is the same as a double but uses slightly smaller rings giving a lower gearing, thus making hills a little easier, same as a triple. It all comes down to personal preference at the end of the day.
Hope that helps
