Where should I start?
'The Most Beautiful Girl In Town and other stories' was where I started, although it's been a few years since I read it. From memory, the stories 'Six inches' and 'The F___ Machine' were quite entertaining(perhaps it's the titles that have most stuck in my mind?). I carried on with 'Women', but I think I'd suggest the short stories first to see how you go - he's a weird one, for sure. Have fun, Chris.
The short stories are a good start, but "Factotum" and "Post Office" are both well worth a go, and they're really short! It's also worth seeing if you can find a copy of the film "Tales of Ordinary Madness" with Ben Gazzarra, from his definitive short story collection "Erections, Ejeculations and other tales of ordinary madness". Shows what Bukowski was about without even having to read a word, unlike the terrible "Barfly"!