I wouldn't and mostly if the offers and discounts sound too good to be true. If the store has open commentaries and good ratings then yes, I will use it.
Of course I would definitely buy from a new store. In my opinion, most of new opened stores sell some of the best quality products (on their level). I believe it is because they are using the "First Impression is Important" belief. So if they sell good quality products the first time, people might recommend their products to other people and that is a plus for them because it's a free promotion and advertising to their new opened store.
It depends on what the store is. If it sells food, probably i will try what they are selling. But i it's gadgets or clothes. Maybe i'll pass.