Here's my prioritized list, given how you've described your circumstances:
1) Computer. Often unavailable, or overly expensive, to rent. Lightweight and easy to take away on holiday. Aids safety and encourages independance from the 'sheep' mentality of following a divemaster or more experienced buddy. No later requirement to buy a depth gauge for your regulator set.
2) Regulator. Safety and security of having your own (well maintained) regulators. Own purchases are likely (hopefully) to be of better specification than average rental regulators. Can customize mouthpieces for better comfort.
3) BCD. Rentals can sometimes be threadbare, uncomfortable and/or a poor fit. Having your own BCD ensures comfort and quality of the BCD. Own purchases are likely (hopefully) to be of better specification and condition than most rental BCDs. Definitely consider a Backplate & Wing (BP&W) design BCD. There are many threads here dealing with jacket vs BP&W bcds.
4) Wet/Drysuit. You stated you were diving "all over", so there is little point investing in a wet/drysuit that will not be practical in different environments. Wetsuit rental is cheap in holiday destinations. The heaviest and bulkiest item to travel with.
5) Underwater Camera Housing. Not an 'essential' by any means - but getting an underwater housing to fit you digital camera can lead to great fun and memories. Your facebook albums will be bulging with great pics in no time! Renting cameras (you won't be able to rent just a housing for your camera) is expensive.
Just for your interest, there is another simular currently active thread
(New to diving. What to buy first?) that may also aid you.