When I was 12 or 13, my older brother played two albums in the car on a long journey home that made me genuinely worried about his aesthetic judgment, to say nothing of his mental and moral wellbeing. I'm not sure if I actually said, "This isn't music", but that's what I was thinking. I felt badly let down. Until that moment I'd trusted my brother's musical taste implicitly, and he had guided me straight and true. But now he was veering crazily towards the jagged rocks of cultural degeneracy and I was being dragged along with him.

One of the albums was, in retrospect, an extremely tame introduction to dance music, which I was wary of at the time: Connected by Stereo MCs. The other album, Bone Machine by Tom Waits, was anything but tame. I listened to Earth Died Screaming open-mouthed, trying to reconcile that deranged, animal howl and the tool-shed clattering in the background with what I understood to be music. I totally failed to get it.

When a friend raved to me about Waits a few years later, I was more prepared to take it on. Now the gravel voice and the drunk and disorderly accompaniments seemed beguiling and beautiful. I can't help thinking about my change of heart in terms of a child progressing from sweet to savoury in its taste preferences: this was the equivalent of picking up a hunk of roquefort or a lamb's kidney instead of a lollipop.

However, my favourite Tom Waits album isn't Bone Machine, it's Rain Dogs – although to be honest I had to go back and retrieve its contents from the marvellous melange that Waits's three career-topping records in the 80s have formed in my brain, the other two being Swordfishtrombones and Frank's Wild Years. (Damn it, no Cold, Cold Ground, no Innocent When You Dream, no Telephone Call from Istanbul…)

I can't choose all three albums as my all-time favourite, so Rain Dogs – the best by a snout – clinches it. Waits had refreshed his sound on Swordfishtrombones two years earlier by moving beyond piano and guitar to dabble with a wider variety of instruments, and on Rain Dogs his repertoire continued to expand, with pump organs, accordions and bowed saws. He also gained the talents of guitarist Marc Ribot, whose humid Cuban licks on Jockey Full of Bourbon perfectly complement Waits's suave dishevelment.

The range of musical styles sprawled, too, and Rain Dogs contains cabaret numbers, country songs, gospel, polkas, ballads and sea shanties. Waits is a sucker for the theatrical, and the ragbag cast here is at the carnivalesque end of things, plus sad-eyed dames and a girl with tattooed tear – "one for every year he's away, she said" – at the late-night, romantically downbeat, Edward Hopper-ish end. (Most of the album was written in a lower Manhattan basement.)

Waits can be extremely funny – I love the hilariously grotesque lineup of stingy senior relatives on Cemetery Polka – but he can also rein in his more bacchanalian impulses and write spare, heartbreakingly beautiful songs, such as Hang Down Your Head, that always make me want to shush people, when one comes on, so that they can experience it with the degree of reverence that I, with a convert's zeal, believe it deserves.

• You can write your own review of this record on our brand new album pages: once you're signed into the Guardian website, visit the album's dedicated page.

Or you could simply star rate it, or add it to one of your album lists. There are more than 3m new pages for you to explore as well as 600,000-plus artists' pages – so simply find their albums and get to work …