You definitely need to know more than a rear axle ratio to choose the transmisison...
There are about a half dozen variables that go into figuring rear axle ratio, and or transmission choice.
I'll list some of the variables from usually the more fixed ones, and finish up with the more flexible ones.
..What vehicle, big or small as far as wind resistance?
..Weight, both empty, and loaded, and or towing something?
..How fast or slow do you drive most of the time, usually this is cruising speed on the highway empty.
..Do you need performance or mileage?
..Engine, what HP and torque, and at what RPMs are the peaks?
..Tire size?
..Transmission and it's high gear ratio? don't forget the low gear either, and for that matter, the rest of them too..
..Rear axle ratio?
Now, considering all that, plug some numbers into the calculator here:
http://www.onlineconversion.com/bigger_tires.htm I like the last one on the page.
Just as an example (one that is way to long

) I'll go through how I figured out what ratios and components I needed in my truck.
I started by picking the engine, a 4-53T Detroit Diesel, approx 175 HP at 2800 RPM and 435 lb-ft at 1800 rpm.
Then I picked the truck, I wanted a work truck, and to be able to comfortably pull trailers, even goose-neck trailers, so a 1 ton was a minimum, then considering frame strength a short wheelbase 2 ton was next in line, and I ended up with a long wheelbase 2 ton, should suit me just fine for overall size, weight capacity, and bed space.
Next is cruising speed empty on the highway, I like 70 mph or just a few faster, and when towing 65 is fine as a top speed.
Tire size is 9R22.5 which turn out to be approx 38" outside diameter.
Empty weight is next, and somewhat difficult to estimate or figure because I am assembling a truck from scratch. My goal is to be well under 10,000lb, hopefully 7,500 tops. This is within the ability of the engine to still get reasonable mileage at speed when empty.
I want mileage when empty, but no sacrifice on towing ability either, drag racing is not the goal.
Lastly came transmission and rear axle gear ratio choice.
I choose the 10 speed for it's close shifts, only a 500 rpm drop when shifting at about 2500 rpm, equally spaced for all 10 gears.
I had the option of direct drive, or 0.80 OD.
Rear axle is a Dana 70HD, and available ratios are 3.54. 3.73, 4.11, 4.56, and a few slower yet, up to 7.something.
Now is when the gear calculator link comes in.
Enter 70 mph, 4.56 ratio (what I have already), Transmission as 1 (what I had to start with), tire diameter 38", and leave transfer case empty, as I don't have one, and default is 1:1.
Click "compute" and I get 2,822 rpm. this is at governed speed for my engine, so there is no more to get, and fuel economy is only an idea, I'll never see it like that.
Now change some variables, we already know I can get 3.54 axle gears, so let's re compute with that figure.
We get 2,191 rpm, which is good when loaded, but not so good for mileage.
Best mileage will be found when the engine is at at or just above the RPM that it makes it's peak torque, in this case 1,800 rpm. This is assuming the engine has enough power and torque to comfortably do the job, and from prior experience and talking to folks who have similar setups I know it does in this case. (if I wanted to go 90 mph, or it weighed 15,000 lb it may not)
So, lets give it a try with an OD transmission, with 0.80 ratio (the only available for my choice of transmission)
this gives 1,752, so a little slow and the engine may be lugging, which hurts fuel mileage and engine life.
then bump up the speed to 72 mph, which I am still comfortable at
we get 1,802 rpm, about ideal.
Now, lets figure I drop down to 65 mph and in direct gear (9th) for towing.
This gives 2,034, which is good, but perhaps on the slow side.
Now, re figure for 3.73 axle gears, the next slower choice, will it bring up both the cruising in OD RPM, and the towing RPM to better suit the engine and truck?
Cruising is 1,846 (at 70 in OD), just about right.
Towing is 2,143 rpm (at 65 in direct), just about right.
So now, looks like I figured what I need, 3.73 gears, 0.80 OD, and 38" tires.
Then comes the trial and error and second opinions..
I bought, worked on, and drove across the country (3 times) both empty and loaded, a very similar truck. Differences being it had a 6V53T good for 250-300 HP but same peak HP and torque RPMs, and weighed 10,000 lb empty. It had the same 10 speed with 0.80 OD, 3.73 gears, and 38" tires.
In driving it it was fine when loaded, but really needed one more gear when empty and cruising, especially out west where the speed limits are a tad higher, but even here in the mountains it could have used another higher gear.
So comparing it to the truck I am building it weighs more, and has the slower gears, but more HP. So I figure my truck will weigh less, which makes up for the lack of HP, then I can get away with the fast gears the other truck needed.
So that's my plan, 0.80 OD, 3.54 rear axle gears, and 38" tires, to cruise just over 70, or faster if out west, and tow at 65.
If I find it is geared to fast my fall back is a 3.73 gear. I will be able to try them out before actually changing rear axle gears by swapping to 36" tires, some low pro 22.5" with the 3.54 gears will be the same as my 38" tires with 3.73 gears.
Also to consider is I will eventually update my engine and it's peak HP and torque will then be at 2,500 rpm and 1,500 RPM respectively. Then I will have more confidence that the 3.54 gears will be about right.
Sorry it's so long and drawn out, but picking gears is not as simple as you would hope it to be, at least not if you know what you want the truck to do for you.
Grigg