Understand first that Tom Waits has several distinct periods in his sound. In the 70s he has a crooner and beatnik style that might evoke images of bar rooms and wacky poetry readings. In the 80s, he started playing around more with his voice and using 'found' sounds and odd instrumentation. In the 90s he took that to an extreme for a while. In the late 90s he started releasing more 'ballads' alongside the experimental stuff (Mule Variations through Blood Money). Since then he's been all over the place. He's like a wacky old man making noise, beatboxing, etc. But he still has a soft side to him. All of these periods are enjoyable, but the point here is that you never know what you're going to get, so honestly you could stab in the dark and pick any album and it won't tell you for sure how much you'd like another by Waits.
I would recommend starting with Rain Dogs, which is his most well-known album (In my opinion also his best, but his discography is huge so it may not be yours). If you like it, ask for more songs similar to the songs you like most on it. I discovered Tom through RateYourMusic. Don't take the ratings by gospel, but you can get a good idea what order to listen to things in if you want to go by 'quality' by sorting his albums by Average rating here: https://rateyourmusic.com/artist/tom_waits
Be aware that Rain Dogs is part of a (loose) trilogy of albums (including Swordfishtrombones and Frank's Wild Years) so you might want to listen to all three. Similarly, Alice and Blood Money are sister albums.
Alternately, if you are the type of person who enjoys watching how an artist progresses, Tom Waits is a pretty great artist to get in to chronologically since his style has changed so much over the years without losing any personality.
I'm throwing my vote in for Swordfishtrombones. Just did an episode about that album with author Willy Vlautin (and musician with the Delines).
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https://www.podomatic.com/podcasts/recordsrevisited/episodes/2019-07-08T18_41_42-07_00
On the Orphans 3 disc set, Tom reads a Buk poem called Nirvana over some ambient organ music...
There's also a YouTube video of him reading The Laughing Heart.
That link has some nice quotes and will get you to both the readings...
folk rock, 90s indie, most 60s pop, softer post-punk music, post-rock, video game music, brazilian music in general
https://rateyourmusic.com/~jsh357
For the record I love Swordfishtrombones. I just think Mule Variations is a weak/dull album that I can honestly never get through in a sitting.
You can listen to the full show here: https://archive.org/details/TheCompleteTomWaitsUnplugged/
There's also a unofficial CD that was released earlier this year. It's easy to find in stores (I saw it at Sunrise Records last week) and also on amazon/ebay. https://www.amazon.ca/Storytellers-TOM-WAITS/dp/B07Z75BXX4