It's nice to have your own gear, and if you can afford it, and you plan to keep diving in the future then they are worthwhile investments but I do not necessarily recommend buying them in advance of certification. Also do not be pushed by salespeople into buying anything that you do not want, but they say you need, unless you know you want them. Rental gear is usually sufficient for the training, and I've seen plenty of people get half way through their training and realise they don't actually want to continue.
Yes - having your own mask, fins and exposure suit is great, but I would personally hold off on investing what might amount to several hundred dollars until you actually know what you need. These items can become very personal (I almost wept when somebody crushed my favourite mask with a tank) and they need to be correct for *you* not what your instructor thinks is correct. Consider also that if your rental equipment is not perfect, then being able to confidently deal with those problems makes you more confident underwater, just in case your perfectly fitting mask springs a leak one day. When it comes to equipment, try before you buy if possible, and don't forget, a good diver should be able to dive confidently regardless of the equipment they are wearing.
Also don't forget that you are going on vacation - if you buy a lot of stuff make sure your excess baggage allows it!
Defnitely do as much homework in advance as possible. There is a huge amount of material available and although you don't specify the agency, the PADI Open Water manual (for example) covers a huge amount of information that is not actually required for certification, but is invaluable nonetheless.
Defintely relax and enjoy and have fun! Some of the skills may take some time to master so don't beat yourself up if you don't get it right first time. Have confidence in your instructor and if your instructor does not make you feel confident, find another one. Don't be pushed into doing something you are not comfortable with. If necessary, ask to repeat things for practice.
Welcome to the underwater world! You may end up like me - I walked into the water 12 years ago and never really left... enjoy it, it's awesome!
Cheers,
C.