The simplest and easiest method of turboing the X1/9 is to fit the MkI Uno Turbo lump which just happens to be the same block (mounting point wise at least) as the 1500 engine used in the X1/9.
If you want to go giant killing I strongly recommend you do not bother trying to convert your 1300 engine. The thermal load is seriously big and without the little modifications in the turbo engine you will cook everything before you get past the 100bhp mark. The compression ratio you need will depend on what boost you want to run and what cam profile you use - anything more than an 8:1 ratio is going to be problematic.
The MkI UT engine will happily tune up to about 150bhp on stock components (including the diddy little IHI turbocharger). At 150bhp in an X1/9 with some suspension upgrades and a bit of a diet you should find that most of those 2l and 3l cars are no longer a problem - unless we are talking about riced up jap street racers.
If you want to take on the really big boys then you need to build a slightly more exotic engine (Punto GT block, MkI UT head, GT crank, pistons and rods, etc.). On a Garett T25 you should be able to reach 230bhp and with more mid-range torque than those FWD ricers can cope with. If you got the diet correct for your car that should be getting on for 300bhp/tonne in a beautifully balanced chassis. You'll need some reinforcement in places but nothing serious (a rollcage would be a good idea though).
For more than 230bhp you need to start looking at a T28 and this is where it all starts to go wrong - The T28 simply won't fit in the X1/9 engine bay. You would have to sacrifice some (or all) of your rear boot.
You're biggest problem is the water radiator (needs to be replaced with an aluminium double core), the oil cooler (use a Delta HF Turbo cooler) and the intercooler (again the Delta HF Turbo is your friend). Finding the items can be tricky but locating them in the engine bay is a nightmare. I've seen them shoehorned in but this is worse than useless as you need proper airflow through them and around the engine. You can open up the sidepods on the X1/9 to great effect and then you can put one of the additional coolers each side but you still need a cold air feed for the induction system.
If you fancy going a bit overboard there is always the option of using the rear deck from the Abarth Prototipo (look up Guy Moerenhout at
http://www.abarth-gmr.be) and a snorkle to match. You could get just the snorkle by itself but it looks more than a bit lame fitted to the standard engine cover.
If you do choose to sacrifice the rear boot your options are much broader. Not only can you move the turbo clear of the engine, you can have some nice proper bananas on a short extractor manifold and you get the benefit of not superheating the engine bay.
Ultimately this is an engine swap and as with all engine swaps you need to be a little inventive. Just remember that you need a lot of air flow and you won't go too far wrong.