Let me start with a lame statement that any design is just a set of compromises. The transformer is even more so.
The most wide spread fallacy about the transformers is the idea that their voltage gain is free. Wrong!!! Here is a little write up on the noise considerations in transformers I posted on the groupdiy forum not long ago. That was about ribbon microphone transformers, but the same rules can be applied to any transformer. Since I wrote it myself, I don't have to ask anybody's permission just to paste it

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Some more on how winding DCRs affect noise. Any resistance is a noise and the problem with high step up transformers is the primary resistance gets multiplied by the turn ratio square.
Say, a typical Chinese ribbon transformer has Pri DCR=0.3 Ohm, Sec DCR=90 Ohm, and ratio 1:55. The primary translated into the output will be already 0.3 x 55^=907.5 Ohm. Add to this the secondary DCR and we get 997.5 Ohm of pure noise.
Another element of the noise increase is lower output due to the series losses (think of it as a resistive divider). You can see with 1.5K typical input impedance of preamp the losses can be quire considerable.
Now let's take a low DCR transformer with Pri DCR=0.002 Ohm, and Sec DCR=6 Ohm (for 1:55 ratio). 0.002 x 55^=6.05 Ohm+6=12.05 Ohm, which also adds very little to the series losses.
But we forgot that the ribbon itself also has resistance (noise). Typical DCR (or for practical purposes, impedance) of a large ribbon of 1.8 um is about 0.15 Ohm. Translated into output it becomes 0.15 x 55^=453.75 Ohm, which leaves us with total resistance in Chinese transformer 453.75+997.5=~1.45 KOhm, and with low DCR transformer 453.75+12.05=465.8 Ohm.
Another consideration is output impedance. In the modern equipment the rule of thumb is the input impedance of next stage should be 5 times highr the output impedance of preceding stage. Most of the preamps are 1.5K in, so the output stage should provide 300 Ohm.
Say, you have a tube microphone with a tube's plate impedance of say, 12K. We take a nice off shelf transformer of 6.5:1. Our output impedance will be 12,000:6.5^=284.02. Close enough.
Don't forget, if you are using say, 6.5:1 then it is actually STEP DOWN... meaning with 32:1 you will get very low output impedance (which we won't need), and also you will lose about 14dB of gain.
The next consideration is input impedance. For example if the source impedance is 0.2 Ohm (ribbon microphone) we don't need high inductance to get a good bass response. When we are going to 10K range, then even we will need much turns, which translates into high DCR (look at the first writeup about DCR). On top of that with special tricks (which greatly increase the price) we will need to fight high capacitance, leakage, etc.etc.etc.
It is an art in itself to make a good and highly optimized for a given application audio transformer!
Best, M