What is the most affordable means of storing 3,000+ gallons (11,000+ litre) of rain water?
Single large tanks
They sell plastic water tanks in the $1000 range for 3000 gallons (11000 litre).  Two such tanks were famously seen in Breaking Bad season 4, as the repository for both the magic “methylamine” they needed, and also for the (spoiler alert).
Figure on 8 foot (2.4 metre) diameter x 10 feet (3 metre) tall.
These tanks are absolutely enormous and come on a flat bed truck; the trucker will expect you to have a backhoe and rigging necessary to pick the tank off the back of the truck.
You could probably fetch one yourself, e.g. if you found a bargain on Craigslist; but to move it we’re talking a big 8 foot (2.4 metre) wide 2-3 axle trailer with a Reese hitch, and a big macho vehicle to pull it.  It’s not the weight, it’s the wind resistance - you don’t want your trailer or tow vehicle tossed out of control or flipped over entirely!

Arrays of small tanks
Country folk have a single “go-to” container: the  “intermediate bulk container” or IBC Tote. These are pallet-sized (40 x 48”, 1 × 1.2 metre) and hold usually 275 or 330 gallons (1040 or 1250 litre; note: multiples of 55-gallon / 208 litre drums). They are 4-5 feet (1.2-1.5 metre) tall.
Now, you can buy these new if you really, really, really want to... and I’m sure factories get quite a good price on them by the trainload. But the people proffering them in single quantity really stick it to ya - they’d brazenly charge $4 for a 2-liter soda-style bottle. (You can get ‘em full of soda for $2).
On the other hand, they’re usually single-use containers, especially food-grade ones, so industry winds up with a whole lot of ‘em.   Now, some clever people on Craigslist will clean them out for you and sell them to you for $35 to $75, but your best bet is call around to industry and service providers, and see who has way too many of them and will let you have em for nothin’.
I recently had a need for one, and a friend immediately offered me one from his workplace’s overstock, and driving through the local sawmill I saw another 30 or 40 piled up.