I have a standard ratio gear set in my gearbox that I have used for years without dramas but I also have a Cooper S ratio gear set available (practically brand new), both have 3.44:1 diffs/final drive.
It is going under a large bore engine that will have a fair amount of get up and go , well much more than before.

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http://www.youtube.com/watch?v=nDMkVq1jRGU

S gears are better.
1-2-3 are all taller by 1/17 compared to the others. 4th is still the same.
I had std K gears in the wife's S replica, definitely not as good ratios as S ones in my 1360.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

So Docmini you think you can utilise the power/torque better with the "S" gearset? It is going under an engine of similar size to yours, not sure of your engine spec but they maybe similar

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http://www.youtube.com/watch?v=nDMkVq1jRGU

My 1360 with S ratios lights the A008s up at 4500 in 1st, if I idle away from rest then tramp it. OK so I do run a 3.647 diff.. next time it's out a 3.44 might go back in.
The 1412 I built (113lb/ft torque) has S gears and a 3.44 diff. Not been put in a car, yet.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Do you build your own engines Doc, or does someone do them for you?

I keep hearing about this 1360 of yours........I'm scared it's going to come and kill me in my sleep the myth is so big!

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"I'm sorry, but a lack of planning on your part does not constitute an emergency on my part!"

Yes I do build my own.
I get GR to bore the block ,balance the crank and grind the cam.
Spiro (St George Crankshafts) grinds the crank.

But the Mk1 S EN40B crank in my 1360 hasn't been reground in the last 30 years, it's been in 3 of my motors and is still at -.010"/-.010" sizes.
Bugger won't wear...

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

What usually suggests one set of ratios to another is the engines power band. The more you soup it up, usually the narower the power band gets, so you need ratios that are closer to each other. So I would suggest working out what your usable power band and rev limits are and then either calculating the useful ratios or ploting them on a graph, be sure to use overall ratios (including the diff).

+ wheel/tyre size?

Actually, yes, but I left that out because generally the wheel sizes on a mini don't vary that much.

Mk1 Mini boxes are the worst (widest) ratios because with no synchro on 1st, they geared it so you could potter off in 2nd. 1st was for `pulling an elephant out of quicksand'.
Wasn't only BMC did this, everybody in UK did back then.
Mk1 S had the best ratios but the 3 synchro boxes were fragile with big power. Can you say stripped 2nd gear, stripped 3rd gear...

If your engine is a 1275 with an all synchro box, IMO it should get Mk2 S gears if you can afford it. They are not that `close' (hardly SCCR!) but better than the stock ones.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

http://www.youtube.com/watch?v=Rh9Gr8fhinI

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No offence intended here but--> anyone writing a book about minis 30 years ago may not have experienced such worn or stuffed-with components as we are finding these days.

You should put your heart & soul into everything you do.

I wish.....even a 5 speed would be nice....

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http://www.youtube.com/watch?v=nDMkVq1jRGU

Since you are going to have high HP & Torque, go for a 3.1 (19/59) or a 2.76 (21/58) diff ratio. you'll love it on the highway & plenty of top speed.

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Have a Nice Day.
If already having a nice day please disregard.