Don't take too much
It's easy to take lots of spares, food, jerry cans, and other stuff on a long crossing like this, weighing your boat down and making it much more difficult to deal with rough weather. The storm we encountered on 19 April reinforced the importance of having clean decks and a light boat.
But, don't take too little
When it comes to spares, all that you really, really need are things you simply cannot live without. At the very top of this list would be tools and supplies for keeping the water out and for repairing your rig and sails. Everything else --- refrigeration, electricity, beer, etc. --- is just a luxury.
If most of what you've done is coastal sailing and an occasional overnight crossing or race, the amount of wear and tear on your rig and especially, on your sails, will be far greater than what you're used to. Weeks on weeks of big ocean waves, rolling around in the swell, gale force winds, and all the other things the sea can throw at you takes a toll on what makes your boat go. Be sure you have lots of extra sail cloth of all weights and sizes used on your boat. You will also need high quality thread and a sewing kit or machine. We did not have a machine and did not miss it.
Be sure that you have a spare for every piece of running rigging on the boat, as well as every shackle and block.
Cats Paw has a single-lined reefing system, which by-and-large worked very well. However, in the downwind sailing conditions of the trades, there were problems. With the boom way out, it put all the bunts and folds of the mainsail as well as bights of line in the reefing system very close to all the rigging paraphernalia on the mast, such as rope clutches, winches, and cleats. Add a good gust of wind (which, after all, is why you're reefing), and it was very easy to catch a bight of line or sail on something, requiring a trip, sometimes several trips, forward. This was especially a problem at night.
The single-line system was also subject to a lot of chafe at the reefing grommets because the line pulls more out than down, requiring a lot of tension in order to get a good tight leach. I've taken to threading tubular nylon webbing over the reefing lines where they go through the grommet, in order to protect them from chafe.
If I had to do it all over again, I'd probably just stick with a simple slab reefing system and granny bars, and accept the inevitable trips forward.
It can be surprisingly cool the first week out of California or Mexico. You will definitely need warm fleece and foul weather gear.
But, just when you're getting used to that, it will become unbearably hot. So hot, you will dread going out on deck for a watch. Be sure to have some kind of shade over the cockpit or pulling a three-hour midday watch will be torture!
The heat also sucks the energy out of you, making the simplest maintenance task an act of sheer self-discipline. Don't expect to be building and repairing your boat along the way. You'll stick to the bare minimum until landfall.
The Marqueasas in April and May are also extremely hot (and humid). It beats me how those ancient cultures built all those maraes in that heat!
Some sort of shade for your boat is essential --- at least a bimini. We used awnings from Shade Tree of Elberta, Alabama. They are of excellent quality and quick to put up. They are very effective at cooling the cabin and doubling your living area by making the boat deck comfortable in the middle of the day. While we got awnings for both fore and aft of the mast, in practice we only put up the aft awning (click here for an example). You don't really need both.
Fortunately, once June and July roll around and once you get a little farther south, the weather becomes delightful. Warm days and balmy nights!
A lot of boats went through a lot of fuel during their crossing and were shocked to discover that the sole service station on Hiva Oa wouldn't sell them any diesel. So, they sat in that miserable harbor for days, waiting for the next fuel shipment. Assume you won't get any fuel until you get to Nuka Hiva. At both places you will probably have to jerry jug the diesel (definitely at Hiva Oa; the very brave may try stern-to refueling at Nuka Hiva).
There are plenty of supplies at both places, but not much variety. The costs will be also be high. You will have to be especially creative about finding fresh fruit and vegetables.
The Tuomotus also have scanty supplies and refueling is even more difficult.
You can get every thing you could possibly want and a lot of things you don't in Papeete, albeit at great expense. The easiest place to refuel is at the fuel dock at the Marina Taina at Maeva Beach. Manager Phillipe is very helpful.