Have some one start the car whilst you're stand in front with the hood open - try to see if you can find out where the noise is coming from. The 1.8 uses two timing chains which are at the very front on the engine and are known to rattle on a cold start - it's a good idea to get the chains fixed ASAP because if they fail you'll probably end up with a damaged head, pistons & valves.
It's also possible for the serpentine belt idler & tensioner pulleys or the fan pulley to make a noise at start up - so I would suggest you remove the belts and spin the pulleys by hand, they should spin smoothly & silently, any noise, any roughness is a sign of a bad bearing - the bearings in the idler & tensioner pulleys are replaceable - you can also start the engine without the belts to see if the noise is still present, just don't run it for more than a few minutes.