The main issue you'll have is the exhaust manifold/downpipe, but you would have the same trouble fitting a 1.8 16v from a MK2!
You could fit the oem digi injection system from the MK3, or fit the KR injection system from a MK2, either way has its strengths & weaknesses. Running the ABF with KR injection results in a really strong engine with lots of power 'out of the box' and is relatively simple. Though you can't really do alot to it in terms of remapping, liek you can with the ABF setup.
If you shop around a nice ABF block on its own will set you back around £200, and the KR setup can be bought for peanuts. As long as you get it all including the inlet manifold, wur, airbox etc etc then it all bolts up directly to the ABF!
The fuel lines need moving over to the driver side though, or you could spend just over £100 on a set of special 16v conversion lines from crazyquiffs MK1 Golf emporium, but you'll probably want to do this anyway as by now the MK1 GTI fuel lines are a bit crispy! Check the fuel filler neck for rust too, as you'll want that replaced and the tank cleaned out before you fit the shiny new lines.
Then you need to fit the top half of the MK2 KR airbox to the bottom half of the old MK1 airbox, and swap the fuel filter bracket over then chop up the lower part of the airbox to make it sit on the MK1 chassis leg, then move the washer bottle to the passenger side.
Last issue is the block height, you may have to do a little persuading on the bonnet to make it clear the throttle body, the other option is to either fit a 1.8 16v lump which is the same height as the MK1 block, or the 9a/6a 2.0 16v lump from a Corrado/Passat/Audi.
If you do fit a 9a lump, swap in a KR inlet cam to bring up the stock 135BHP to 150+ BHP

The conversion is actually pretty much a bolt off, bolt on affair, and is pretty easy since there isn't much fabrication work involved.
edit: check out this 1.3 MK1 build page, explains it all nicely! Ignore the bits about messing around with the steering rack, wishbones, gear linkages and chopping off the engine mount bracket, as you already have a GTI so all this work is not required
http://www.clubgti.com/forum/showthread.php?t=69825