mate i dont know much about heater core etc, but so far as the actual cooling system is concerned, three main possibilites (that ive fixed on my car in the last 12 months)
1.radiator hoses
2. radiator side tanks or less likly, the alluminuim (i think) core
3. the bearing seal in your water pump
if its the radiator hoses, pretty easy to spot. if they are craked/perishing, its a lilky culprit. and even if they arent leaking, but look like shite, replace them anyway, about 20 bucks. ive got a series 3 ( i swear thats what it says in my manual) so that thermostat cover uses a gasket, not an o ring like in the series 1, that could be worth looking at too if its perished
if its the radiator itself, run the engine for about 10 mins or however long it takes to warm up, keep an eye on the radiator, if it starts pissing out coolant anywhere on the radiator, its a new one, normally about 130 too 200 from repco, plus new coolant, simple job, you wont need anything more than a spannner to take off the cooling fan, a screw driver and a set of pliers for the retaining clips. make sure you gte the right radiator but. and dont use radiator stopleak, it cloggs up your engine, if the leak is small enough, my mechanic suggested to me cracked pepper added to the coolant as a tempory solution, i didnt try that one either
the bearing seal on the water pump, i doubt this one is the case, because it shouldnt leak as much coolant as you described, but there is a weep hole on the underside of the pump pully, if coolant is coming out it, a sign that the seal is ratshit, and the pump needs replacing immedialty, the coolant will leak down and dry, showing as a white residue generally, or get a little mirror and check on the underside of the pully for coolant. this job is pretty easy to, but its alot more of a fiddle. a new water pump will set you back about 140 from repco.
also check the heater hoses in your engine bay. oh and i forgot if your oil has milky colour in it, or there is oil in your coolant, you ve got a stuffed head gasket. if thats the case you're probably best off leaving it to your mech