If you are looking to maintain the pressure through smaller tubing, you will want to get a pump with a high head pressure (the height the pump can push and maintain water vertically). A high GPH is good but if it has a low head pressure, it will crap out when pushing liquid through a smaller diameter. i.e a 100GPH 20' HP pump will put more pressure out then a 200GPH pump with 10' HP. A higher head pressure would also be better due to the fact that most of the immersion wort coolers are generally pretty tall and unless the pump is located above the cooler, it will have to work harder to get the liquid flowing.
A workaround of course would be to use a pump that has a 3/8" ID output, this will help maintain a steady and constant flow/pressure through the line. Aquarium pumps are a good example.
If the water is coming out cold, it is moving too fast for the heat transfer to occur, it should come out warm, maybe slightly warmer then ambient.
I'm not going to lie and say I have any experience with immersion wort chillers, because I do not (complete HB noobie), however I do have about 6 years experience watercooling computers and the same rules apply.
A simple closed loop with pump--> chiller--> large bucket of ice water, would be very simple to make. The most efficent would probably be using 1/2" ID copper and plastic tubing, although that corragated copper tubing looks very promising also (more surface area in contact with the wort).
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