There is another question in the site, in which the OP asked:
Where on Earth is best to build a large underwater lab complex?
One of the obvious ideas for the location of a large laboratory would be underwater, where you don't have to hide it under some alternative identity to keep people away and there are far fewer rules and regulations to deal with outside of the ones you set yourself. So, assuming I have the resources to build such a place, where would be my best options to construct it if I want to take advantage of as many natural resources as possible?
My answer there contains some parts which could be reused here, with some modifications. About being secretive:
It is exactly because you don't have a cover up that you will get prying eyes. What do your goons tell the dock officers when they get asked about the destination for all those tons of fertilizer?
Instead, find or found some legitimate business that can only be conducted very far from the shore, and then you can buy all the supplies you need with practically no questions asked.
If you do wish to live strictly in an oil field, you won't have the resources to feed everyone just off of it. But you can trade with unsuspecting nations:
For example, pair your lab up with an oil company. You can build the lab right under an oil platform. The platform provides the fuel, energy, and the facade you need to buy all kinds of tools, chemicals, machinery and other supplies. If you happen to own the platform you can also use its profits to bankroll the lab. Otherwise the lab provides tech and food (for those courageous enough to eat... whatever it is that you do there).
You could get some more resources in an autonomous way if your rig is close to an island:
If you want to go green for whatever reasons, you could find a university that does state-of-the-art technological research (MIT, Caltech) and conduct research on wave power. This way you get paid to build your own generators instead of having to spend your own money on them. Find some Central or South America island to conduct your research - you can use the excuse that you get more solar power that way, also altruistically you are going to help some poor country with their economy... And then you use the local corruption on your favor, to keep prying eyes away. Bonus if the island happens to be a fiscal haven. Honour the research contracts with your partners, but do keep a couple offices and rooms in the underwater facilities which only a select few mad scientists have the clearance to visit.
If the island is owned by you, either de jure or de facto, it would be even easier. And you can let only the most higher ups live in the rig - the lower citizens would be working on arable land. They might not even know about the whold secret society thing.
And if you don't mind cold weather:
Those still too social for you? Partner with a government and help them build a research station on the south pole. Guaranteed supply deliveries, paid by taxpayer money. Just spend a few thousand dollars building a cute house and drilling ice every few months, write something about gas concentrations on different layers of ice... And they will leave you alone to spend the remaining millions on whatever. Build yourself a nice facility inside Lake Vostok, where not even the most powerful spy sattelites will catch you. Have fun!
In all options above, someone will bankroll you. You can spend the money in supplies to last for decades. The last option saves you a lot in terms of refrigerators, and your stored food, alcohol and drugs would last much longer.