noun which may take the genitive case particle 'no', noun
my kind of; my favorite; to my taste
Used to describe something that suits one's personal taste or preference. Often used in the pattern 私好みの + noun.
このカフェは私好みの雰囲気だ。
This café has an atmosphere that's just my kind of thing.
彼の選曲はいつも私好みだ。
His song selections are always to my taste.
好み means 'taste' or 'preference' in general, while 私好み specifically means 'my taste' or 'my preference'.
Compound of 私 (わたし, 'I') + 好み (ごのみ, 'taste, liking'). The reading ごのみ is the rendaku form of このみ.