Studying logic helps you understand the underlying structure of arguments. I don't personally see it as a prerequisite to reading philosophy, but it can definitely be helpful. However, if you do start with logic, I would stick to the modern logic, rather than the Aristotelian, which is of more historical than practical utility at this point in time.
As far as your second question --everyone will have a different answer. I would argue in favor of starting with Plato and Descartes, in terms of those being two of the figures most universally responded to by subsequent philosophers. (For example, much of Nietzsche is proposed in reaction against Plato, and Kant is widely viewed as a synthesis of Descartes and Hume.) Even if you aren't a fan of those philosophers yourself, reading them will still give you a context to start from --and both have some relatively short, accessible, but central works to start with (Meno, Apology, Symposium for Plato --or even The Republic which is a little longer, but is probably the most famous work of philosophy in the western world; Meditations for Descartes, which arguably comes in second).