Better weaponry will appear as the game progresses. The ships and equipment can be acquired in stations. In contrast to other games you are tied to a single station in the system, so you cannot fly whenever you wish - only when you accept a contract. The travel between systems works much the same - it is one of the options in the contract menu and it is for free. The stations and systems vary in visual appearance, surroundings and equipment and weapons available.
Some systems are more dangerous than others.
Space is filled with all sorts of nebulae, asteroid belts and similar things that make traveling through it more difficult. Some stations offer you an alternative way to make money - gamble for it. You will rarely win, but when you do it will make you a rich man. Every mission is unique and there are no generic missions we used to see in other games. Each mission contributes more or less to the story.