Polish has little in the way of "melody". It's a rigidly syllable-timed language where the rhythm is a rather monotonic "Bam-bam-bam-bam-bam-bam-bum", like a machine gun.
The best way to learn to listen to the language is to listen to audiobooks.
When I was learning Polish in Poland, I was listening to an audiobook where the reader read exactly like a machine gun. Monotonically and with absolutely no variation in pitch or rhythm. To me it sounded odd and mechanical, but when I asked my Polish friends, they didn't find anything remarkable about it.
As an American, you are going to have to get used to the fact that all syllables are pronounced fully with the same length. Stressed syllables are not pronounced longer, and unstressed syllables are not weakened or shortened. Also, word stress is a lot weaker than in American English. This can make it difficult to identify word boundaries until you get used to it.
Poles often sound almost as though they're chirping when the speak. Conversely, this monotonic "bam-bam-bam..." tends to spill over into their English, with almost zero exceptions in my experience.
As the accent is nearly always on the primary vs. the penultimate or even ultimate syllable (except where a noun is spoken in a declined form, e.g. "Ogrod" as opposed to "oGRODu"), it lends the language a kind of jerky or mechanical quality when spoken naturally by a native Polish speaker.
Personally, I find it all quite appealing, making the speaker sound as though they're considering what they're saying, rather than rapid-fire Spanish, for instance, which sounds to me like one long sentence that never stops.
People have told me that Polish sounds like a bunch of 'sh' 'ch' sounds with some vowels interspersed. I've had people think its everything from Russian/Czech/Serbian to some idiots thinking its French or German.
I think though, from my dalliances with Czech, that Polish may well be the language with MORE vowels! For a long time, I thought that no language could beat Polish for tongue twisters, that is, until I discovered Czech:-)
Ooohhh, but watch the false friends! Some might prove fatal, such as Polish "szukac" vs. the Czech sound-alike cognate (not a calque though by any meansLOL), Polish "staly" vs. Czech "staly" etc...