I must admit, though I appreciate Bill a Lot, I'd recommend others:
I'd start with 'Burning in Water Drowning in Flame', the reason is, there are poems from early books (back to the beginning 60s) till the start of the 70s. So it gives some overview anyway. Yet at the same time it's somehow 'complete' in itself.
Also it contains some 'classics', as 'tragedy of the leaves', 'to the whore who took my poems', '2am beer', 'love&fame&death', 'beans with garlic', 'don't come around but if you do', 'class', 'a poorly night', 'the rent's high too', etc.
For the later ones, I, too, would prefer another one:
'You get so Alone at Times that it just makes Sense'. The reason: we see a very 'mature' Bukowski here. Reflecting on his former life as well as on his present one, reflecting his idols in literature, in classical music, etc...
Not sure, if there are 'classics' in it, but recommend very much: 'beasts bounding through time', 'cornered', 'darkness', 'a funny guy', 'final story', 'friends within the darkness', 'the wine of forever', 'party's over' and especially: 'how is your heart?' and 'forget it' (which is double as moving to read now, only one week after March 9th).
So, that's mine.
But I can tell you: everyone has his own favorites. So maybe there are still others to come. It will overflow you.
Maybe it's BEST, to buy one of his Live-Readings. You'd get a glimpse about his sound and tune and his ways and all that. It will never leave you, listening to his voice reading his poems. There's no escape from having some of his readings anyway, so, why not start with them, esp. as a poetry-newbe?
Highly recommended readings: 'Poems and Insults' (1972, San Francisco), 'Solid Citicen' (1978, Germany), 'Hostage' (1980, Redondo Beach).