Go to the police clearance centre, they are used to dealing with foreigners, there are written guides in English, the staff are very friendly and helpful, there is a print shop nearby for the inevitable paperwork. It takes about 2 weeks and you can collect it or have it posted.

Fortune Town has lots of vendors all in one place, main brands and independent. Just make sure to look at the box it comes in so that it is new and genuine. I got a great deal on an Asus there. There are also plenty of stores in the main malls, Emporium has a big computer area with lots of brands, Central World has several flagship stores.