Your country has decided to completely re-design their currency system. For whatever reason, they’ve tasked YOU with deciding what denominations will be minted/printed. You have complete authority here; if you want 43 cent coins, you can have 43 cent coins. Base-12 currency? Yes, please! Go nuts!
What denominations do you want?
Consumer product-based. For example, the minimum denomination would be “one small coffee.” Then “fast food value meal,” “business casual shirt,” and so on up to “brand new washing machine.” When people figure out that a drink at a bar costs the same as a new shirt or a week’s wages = two washing machines, consumer spending will be on a much firmer footing.
I’d want coins in $0.25, $1.00, $2.00 and $5.00 denominations, and then $10, $20, $100 and $500 notes.
I went to the laundromat a couple of weeks ago to wash my comforter and it was a pain in the ass to feed twenty-something quarters in the machine.
Assuming US money …
If we’re being sensible:
The smallest coin is $1, followed by the $5 and $10. The smallest bill is the $25 then the $50. No others.
Any old money not turned in during the next year ceases to be legal tender but may be confiscated on sight by any bank, merchant, or LEO. Let the CTers pop a blood vessel; see if I care.
If we’re being silly:
Coins in prime numbers only: 1, 2, 3, 5, 7, 11, and 13 cents. Bills in prime numbers only starting at $17 up to $97. Which gives 7 denominations of coin and 19 denominations of bill. Instead of pictures of statesmen and presidents the coins will have pictures of farm animals and bills will have pictures of rodents. Bills are the size and thickness of playing cards but printed portrait style, not landscape.
And we’ll revalue the currency at 3.14159 new dollars per old. The new currency symbol to replace “$” will be “,”
Demonetising US dollars is not sensible. You can phase them out, but the US has never demonetised any coin or bill.
You phase the old currency out by insisting it be redeemed at full face value for new currency over a logistically reasonable, but deliberately short, time period. The whole point is to crush the black economy and the vast overseas counterfeit currency supply. Confiscation comes only after the redemption period has expired. Holding old currency would not be a crime; like old stamps they have collector value. But using them as money is verboten.
Besides, that’s all peripheral to my real plan which is the silly one.
I’d make it a felony to possess, pass or encourage the manufacture of dollar and/or two dollar coins. Then keep the rest of the money the same denominations, but a lot more colorful using modern polymers and holographic windows.
Reintroduction of the halfpenny which would be called the halfpence.
I’d pretty much keep the system we have now. 5, 10, 25 cent pieces, and 1 and 2 dollar coins. A five dollar coin presently seems a bit much to me, though in the future who knows. But let me do some research to see if we need the nickel.
For bills, $5, $10, then $25 instead of $20, then $100. Turn the $20 into a $25 bill to be consistent, and the $50 serves no purpose.
I’d also issue bills in unusual denominations to commemorate things. If Wayne Gretzky died, issue a $99 bill in limited edition. For Canada’s 150th birthday next year, issue a $150 bill. Stuff like that, it’d be fun.
Get rid of all currency except the penny, in order to force everyone into electronic payments. That way all transactions would have to be legal and tracked! What a wonderful world it would be! 
Not quite the OP’s question, but US banknotes of all denominations are the same size and color. That’s the first thing I’d change, it’s monumentally stupid.
I would eliminate all cash currency. It would all become digital and tied to your national ID with appropriate biometric safeguards, which would also be required for voting and other civic responsibilities.
I’d like to see paper notes of $500, $200, $100, $50, $20, and $10; and, coins of $5, $2, $1, Half Dollar, Two Dimes, and One Dime.
They fit in my wallet rather well.
I realize you’re discussing Canadian currency. For comparison the US dime is currently worth less than the last coin we abolished: the half-cent. A historically consistent approach to US coinage would have a 20 or 25 cent piece be the smallest now.
IMO it’s a good bet the Canadian nickel is long since obsoleted by inflation.
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Separate topic. …
It occurs to me that what we really ought to do is abolish the bills, not the coins. Cards are the future way to pay for anything bigger than a pittance. So bills are unnecessary. Make 25 cent and $1 coins and be done with it. Make them about the size of current pennies and nickels. Damn near nobody ever needs to carry more than three of 'em. Mandate cards for all transactions in excess of $2 total. Also prohibit sales taxes on cash purchases. The sticker price is the price, period.
Inflation has made the $100 the new $10, so large denominations are needed. Instead of large notes, (or addition to) $50, $100 and $500 coins would be cool, and worth looking under the couch once in a while to boot.
In the US at least, the nickel/five-cent piece costs more than face value to mint (as does the penny/one-cent piece). Between that and the fact that you really can’t buy anything with either coin, there’s no rational reason to keep them in circulation.
Agreed. Ref my “sensible” proposal above.
Depends a lot on whether your goal is facilitate the black economy and the drug market or to impede it.
I believe the logic is kind of specious here (no offense) ; the sort usually favored by politicians and technocrats. Just because something can be used by crooks is never a sufficient reason to make it unlawful? It probably “sounds” like a good idea though, and that seems to be all that’s required these days.
I’m just pointing out that to call a $100 bill a “large denomination” these days is laughable, as anyone who shops for groceries can attest. Bills don’t last particularly long in use, while coins last decades or even longer.