The idea of trying to pronounce the shch in 'fresh cheese' as a first approximation to the Russian Щ strikes me as overkill. All the thing really amounts to is pronouncing sh and bringing air OVER your tongue instead of under it.
Yes, Russian has letters designed to represent Slavic sounds like Щ (shch or the Polish equivalent szcz).
The Slavic and other languages have the sound represented by Ж or ż or in English pronounced like the "J" in the French name "Jacques".
The other hard ones to distinguish are Ч, Ц, and Ш (ts, ch, and sh in English...)
But my Russian sucks...