Now that we have differentiated between transitive and intransitive verbs and have discussed the intransitive ones there must be something about the transitives ones. Yes, you're right, there is. Actually we have to divide the transitive verbs into two different cases:

The direct object following the transitive verbs is something concrete well defined, then the negation is formed with nicht.

Ich kaufe den Stuhl nicht. = I do not buy the chair. Du liest das Buch nicht. = You do not read the book. Er isst den Kuchen nicht. = He does not eat the cake.

Is the direct object not-concrete, not well defined then the negation is formed with kein. It is quite simple to find out, whether it is kein or nicht. You see the English phrases don't use the definite article anymore, nor do the Germans. And this is a very important rule: There are no articles with kein/e/er.

Ich lese keine Bücher = I do not read books. Ich esse keine Miesmuscheln. = I do not eat mussels. Wir sahen keinen See. = We did not see any lake.

In English you could always try to use any in the negated sentence, because if you can use any then the German negation is definitely with kein.

Ich lese keine Bücher = I do not read books. (I don't read any books.) Ich kaufe mir keine Schuhe = I do not buy shoes. (I don't buy any shoes.)

The rule about the articles can be reversed in the way that it is absolutely correct to say: If the German positive sentence uses an indefinite or no article the German negation is with kein. Kein is also used, if before the noun is put andere / anderen (others).

there are = es gibt, whole = ganz (here it's ganzen because it's a direct object, which is discussed more in detail in declension of the adjectives)

Es gibt keine Kartoffeln in der ganzen Stadt. = There are no potatoes in the whole town. Wir haben keine Kartoffel. = We do not have a potatoe. Wir sehen keinen See. = We do not see (any) lake. Ich will kein Buch. = I do not want (any) book. Ich will kein anderes Auto. = I do not want another car.

once more the negatio with nicht

wollen = to want

Ich will dieses Buch nicht. = I do not want this book. Wir wollen ihn nicht sehen. = We do not want to see him. Du mußt ihn nicht kaufen. = You do not have to buy it. Er will den Schrank nicht. = He does not want the closet.