If you are using a sump, then that needs to be connected up before you fill the tank and you will need to have the recirculating pump installed and running. Any biological filtration you plan to use should be setup before you start your 3 month count down. If you are using Live Rock (not a trivial expense and is the only way I recommend setting up a saltwater environment), you have to have it, your bottom substrate (if you are going to use any) and some form of water movement around the rocks (power heads or Koralias are most common).
There are almost as many ways to address cycling a tank as there are aquarists and enrolling in a reef forum will present a number of ideas. The following suggestions are preclassified as IMO and IME and other suggestions are solicited. If you find conflicting opinions, take the safest, not the one you want to hear.
Don't get your rock until your tank is comfortabley where you will be keeping it and you have water to fill it. LR should not be out of water longer than it takes to transfer it to the tank and should NEVER be allowed to get dry. If you buy it locally, bring it home in water or at least wrapped in wet newpaper. If it is shipped, it should come wet wrapped. Dont' unwrap it until you are going to put it in your tank and do that ASAP with enough water in the tank to cover the rock (don't fill your tank all the way or you will overflow the tank when you put in the rock and sand). You can arrange the rock at this time or just leave it well exposed and come back to working with your arrangement over the cycle period. Make it a goal to keep water circulating around as much surface as you can manage.
What you can add over the cycle time:
Protein Skimmer
A protein skimmer is not needed for the initial cycle (and some people recommend against using one initially to speed up the cycle) but IS highly recommended before adding an octopus. If you are using uncycled rock, you should run it the last month of the cycle or extend your cycle an additional month to let it run for a full month. If you start with cycled rock, there will be less protein build up in the tank water but you will want to run it a couple of weeks before introducing the octopus.
Chemical filtration
You can add carbon filtration (either with a filter sock at the sump drain or with a canister filter that is not intended to be used for biological filtration) sometime after the first month. It can be pushed out to the second month but you are likely to start detecting odor from the tank (depending upon your LR and anything you might add to encourage ammonia creation).
Water Treatment
If you are going to create your own RO/DI water and you have a source for it when you fill your tank (you can use distilled or you can get RO/DI from many pet stores or you can buy premixed for the initial fill). You can put off purchasing a unit but life is better when you own your own and you will need to cover the expense of obtaining it either way. You will not be doing regular water changes the first couple of months so you will only need fresh top off water to handle the evaporation. Before adding your octopus, you will want to do a large water change (30% exchanging old saltwater for new saltwater) and then have several gallons of saltwater available for weekly exchanges. During the week you will need to top of the tank with fresh RO/DI water daily or every other day depending upon your evaporation rate. Keeping your tank topped off will keep the salinity constant as well as keeping your skimmer running smoothly without constant adjustments.
Lighting
You can put off purchasing lighting almost indefinitely unless you decide to add corals. Ambient light is fine for all octopuses but without a light over the tank, viewing the animal and photography suffer. I like to keep my curing live rock under normal fluorescent light to preserve some of the plant life and cycle my tanks with a regular light cycle but it is not necessary.
Keep in mind there will be additional expenses, including clean up crew that are part of they cycling procedure.