ga hoshii and tai desu – explanation

Hey there,

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Im learning Japansese by myself and I want to be sure I understand that correctly.

Please confirm or correct me if wrong (I know that *watashi wa* can be ommited but lets just leave it there).

I want to buy a car – 私は車が買いたい です (Watashi wa kuruma ga kaitai desu)I want a car – 私は車が欲しいです (Watashi wa kuruma ga hoshī desu)

but what if I want to put an additional adjective to a car to have something like:

I want to buy **a new** car – 私は新しい車が買いたいです (Watashi wa atarashī kuruma ga kaitai desu)

Is that correct? Is the order atarashii kuruma ok? Do I need any particle there?

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Thanks for any tips.