Per this NGram, large is far more common overall than big and huge put together, so in any context where you're not sure which word to use, treat large as the default.
Also note that parents normally introduce their children to big before large (probably because it seems phonetically simpler and more distinctive). So in later life people may see big as slightly childish/informal, where large appears more "grown-up"/formal.
I suggest avoiding huge unless you really want to emphasise abnormally large. But as @barbara says, there are many alternatives in that case (enormous, gigantic, vast etc.). It's also worth noting that in casual speech, people often use "quirky/unusual" alternatives such as humungous, ginormous, thumping. It's best to avoid those unless you're in company where you notice others doing it.
The only "rule" I can think of to help decide when it's better to choose big over large is that big becomes more likely in contexts which are more metaphorical (as opposed to "literal", when you're talking about the physical size of something).
Thus, there's nothing to choose between a big man and a large man, because that's simply the literal sense. But in...
That was big of him (he did something noble/generous).
It was a big disappointment (it was very disappointing).
He's just bigging himself up (he's trying to make himself appear more important than he really is).
... large would never be used. With OP's specific noun community, the metaphoric "stretch" isn't actually very great (large/big!), and there's really nothing to choose between large and big.
Of course, there will be plenty of exceptions to my above "rule" (as in the relatively recent BrE slang giving it large, being noisily aggressive). So just think of it as a "slight tendency".
Significant means meaningful; it says nothing about magnitude. A small advance may be significant:
Gene analysis based on work done by the publicly funded Human Genome Project may have moved science a small but significant step closer to finding a better treatment for Alzheimer's disease.
By the same token, a large advance may be insignificant:
This tonnage represent a very large advance in airborne volume, but is still insignificant relative to over-the-road volume.
So if you mean significant, write significant - don't replace it with big or large or huge. If however you are talking about magnitude, let usage guide you; consulting a corpus is a very good idea. (But at the BYU site you want COCA, Corpus of Contemporary American Usage, or BNC, British National Corpus, rather than COHA.) Large and big vary idiomatically; huge, however, signifies a much greater magnitude than either of those, amazingly large, and in formal usage will suggest you are speaking hyperbolically unless you can substantiate the choice.
Best Answer
Both huge and large would be acceptable in this situation. Huge would emphasise the size of the cost more, but large would more likely be used in formal contexts.
To describe the cost, you should be using the adjectival form of computation - computational. Given that you are referring to one unique thing (the cost), you should be using the definite article as well. Your sentences would then become: