Want & need
What you want, what you need and what matters, all said with X ga ___.
hoshii
polite hoshii desuwant (a thing)
ほしい ほしいです
Says you want a thing (X ga hoshii); it is an adjective, and for wanting to do something use -tai, for wanting someone else to do it -te hoshii.
atarashii pasokon ga hoshii
I want a new computer.
新しいパソコンがほしい
atarashii pasokon ga hoshii desu
I'd like a new computer.
新しいパソコンがほしいです
Only for your own wants. Asking a superior 'X ga hoshii desu ka?' sounds too direct. To ask for something in a shop, say X o kudasai or X onegaishimasu, not X ga hoshii desu.
Learn alongside: hitsuyou
hitsuyou
polite hitsuyou desunecessary, needed
必要 ひつよう 必要です
Says something is needed (X ga hitsuyou) or not needed (hitsuyou nai), for documents, money, time, skills and steps.
atarashii pasokon ga hitsuyou da na
I'm going to need a new computer.
新しいパソコンが必要だな
atarashii pasokon ga hitsuyou desu
I need a new computer.
新しいパソコンが必要です
Casual 'need' is usually the verb iru (要る): kore iru? / iranai (no need). It sounds like iru (be there), but the negatives differ: iranai = don't need, inai = isn't here.
Learn alongside: hoshii
daiji
polite daiji desuimportant, precious
大事 だいじ 大事です
Says something or someone is important or precious (daiji na hanashi = an important matter), and odaiji ni means 'take care' to someone who is ill.
kazoku ga ichiban daiji da yo
Family matters most.
家族が一番大事だよ
kazoku ga ichiban daiji desu ne
Family matters most, doesn't it?
家族が一番大事ですね
taisetsu is a synonym that sounds warmer and a little more formal; daiji is the everyday spoken choice.