minimal requirements id say one cardio machine, whether its an X-trainer a treadmill or a bike (bikes probably the cheapest) and a set of dumbells, and something to enable you to do situps, i used something like Buy V-fit Doorway Sit-Up Bar. at Argos.co.uk - Your Online Shop for Other gym equipment.
but you must remember it all depends on your goals, if you goal is to get lose weight then the above is good, but if you wanna get hench then obviously your needs are different