"I do not want a purple skirt."
"i" & "no" particles are added to turn noun into adjectives. 5 primary color (Red, Blue, Yellow, White, Black) are "i" adjectives. Red - Aka (noun), Aka"i" ("i" adjective) - Akai kuruma (Red car). Other colors are "no" adjectives. Purple - Murasaki (noun), Murasaki"no" ("no" adjective). Murasaki no kuruma (Purple car), Murasaki iro no kuruma (Purple colored car).
This is a good question that learners like me struggle with. To a non-Japanese speaker, it seems there are a few words that are generally preceded by が where you might otherwise expect は, most commonly "feeling" adjectives like ほしい and 好きい. Sometimes, in negative sentences like this, they're preceded by は. It's not a rule, and I don't know why it happens, but of course nobody seems to have a decent explanation.
Right, you have a good point. I can tell, when a person is fluent enough, he will not be able to tell easily why a grammatical feature is written or spoken like that quite a lot of times. This is the case of は and が where one can only grasp the difference in each scenario when he is very fluent.
The basic idea is this graph - when you have to choose one from a number of choices in the former part of the sentence, use が, and if the choices are in the latter part, use は
You have fixed your topic as スカート. You have two choices ほしい or ほしくない. So スカートはほしくない.
You can say スカートがほしくない, when you have a number of choices スカート, ワンピース, ブラウス and the one you do not want is スカート.
There is really not an obligation to use が with ほしい, いい, 好き, 嫌い, できる, or the potential form.
It would seem that in japanese, many things that would be considered with a subject/verb/object construct in other languages, are instead dealt with using a "property of being the subject of a particular verb" instead. This property belongs to the object rather than being done by the subject and is thus more like an adjective. Objects have the property of being liked or being wanted (by me) for example.