'cz' and 'ć' are very different sounds to Polish people, unfortunately it seems that foreigners have enormous problems with distinguishing them. I'd go with a чесьць transliteration for Cyryllic.
Have a look (listen) here, for quite a good pronunciation of Polish alphabet (disregard the weird 'ch', it's the same as normal 'h'), and in the section 2 there are comparisons between problematic pairs of sounds.
I hear ć in the alphabet as чь (palatalized cz), or maybe as тщ. Can someone confirm/disprove this? It is cirtainly not ць.
After some listening to alphabet I came to some conclusion, that sz, cz are equivalents of cyrillic ш, ч, ś is russian щ, and ć- may be approximated as тщ, the same sound as j/q in Chinese pinyin - https://en.wikipedia.org/wiki/Voiceless_alveolo-palatal_affricate
It is even more challenging for English speakers to learn to produce the ś and ć sounds accurately, as these sounds do not exist in English.
As Dmitry points out, ć is a voiceless alveolo-palatal affricate ⟨t͡ɕ⟩, and ś is a related sound, a voiceless alveolo-palatal sibilant fricative ⟨ɕ⟩ (see https://en.wikipedia.org/wiki/Voiceless_alveolo-palatal_sibilant). As one can tell from the respective IPA symbols, the latter is the same as the former but without the sharp, turbulent articulation.
That is only part of the story, however, because these symbols and descriptions address only where and how the vibrations are generated and do not mention the involvements of the lips, which can vary the resulting sound greatly by affecting the resonance of the mouth. When these sounds occur in Chinese, for example, the shape of the lips is determined by the vowels that follow these consonants. So, in that context it is reasonable that we don't attribute any particular lip involvement to the ⟨t͡ɕ⟩ and ⟨ɕ⟩ sounds. However, in the Polish word "cześć," from what I can hear, the lips need to be rounded (corners tightened), much like when we say "sh" or "ch" in English. Unlike Chinese, though, there seems to be no external determination (by any preceding or following sounds) to shape the lips this way. So, at least in this word cześć, this pursed-lip resonance is part of the characteristic of one or both of the Polish ś and ć sounds themselves. (I have noticed the "ci" (which is also ⟨t͡ɕ⟩) in "ciasteczka" does not involve this lip rounding.)
By the way, a caveat to other Chinese speakers: The examples 豬 in Cantonese and 京 in Mandarin given in https://en.wikipedia.org/wiki/Voiceless_alveolo-palatal_affricate are misidentified. Those are actually voiced consonants. A correct example in Mandarin (and one that uses pursed lips) would be 曲 (qǔ).
I've been thinking about this for a couple of days now... In English, when we say hello, we can say it with different tones of voice. Saying hello in a dull manner would make one assume you're bored or saying it vibrantly would show that you're happy and pleased to see the person. But I can't think of how to pronounce "Cześć" sounding happy, whenever I try I end up screwing the pronunciation up and making it not understandable.
The pronunciation can be tricky since some of the sounds are not present in English, but the orthography is pretty consistent. The four sounds to reproduse are "cz", "e", "ś" and "ć". Check out tips and tricks notes for lessons if you are on PC.
Also here's a very helpful compilation of various discussions about Polish: https://www.duolingo.com/comment/16296174
I bet there is something about pronunciation there too.
Great resource for accurate pronounciation
I think the problem is that for Polish learners of English "hello" usually sounds quite informal. It wasn't until I began to be active here that I understood that it's really pretty... neutral. Neither formal (of course) nor informal.
We will change the main translation of "cześć" to "hi".
Just stick to 'Yak tam" "Czesc" in the phonetic Polish I grew up with means something like "I want it". "It" being the subject that is being discussed. I don't have access to the linquistic letters, but I mean to spell it like it is presented above. So somebody tell me what I mean by saying 'Ja czesc'.