Moving from the UK: I used Transpackship for a door to door service and had no complaints at all. Customs clearance when your goods arrive can be the most hair pulling experience ever, but this also applies to any time you deal with Jamaica Customs service. Be warned, I had items stolen from off the dock as the container was being checked so you need to watch everyone very carefully.
Do not bring large electrical items with you - even if from the UK and you have 240 volt sockets in the Jamaican house. They just do not seem to last in Jamaica. Better to buy locally.
Permanent Residency - just follow the instructions in the PICA website. It took me about a year in total to get the stamp in my passport. They are very strict regarding the paperwork and the interview is not just a friendly chat. Once you have the passport stamp it is easy to get renewed at any PICA office.