How to suggest plurality of a generic word?
Solution 1:
The word "fruit" is a noun. It's an exception where the noun is both countable and uncountable. So the plural of fruit can be either fruit OR fruits.
- When we think of "fruit" as a group collectively and in a non-specific way, then we tend to use the word "fruit" (without the "s").
For example, "I like fruit." (uncountable, meaning fruit in general).
- If you are emphasizing the different kinds of fruit, then you can use "fruits".
For example, "Apples, orange, mangoes!! There are so many fruits to choose from!"
So, out of all three options, the phrase "basket of fruit" seems to suit your example the best since it is the same as saying, "oranges are a fruit". Hence, "basket of oranges" implies "basket of fruit". Another way of saying it could be, "the basket has fruit in it" (here, "fruit" refers to oranges in general).
Solution 2:
There are several answers to this question that address the countability of "fruit" specifically. The longest answer provides examples that cover, with almost excessive thoroughness, differences among possible uses of "fruit" and "fruits". (Note, however, that many of the examples are older and/or more formal texts, so they may not be entirely useful for purposes of this question.) But your question seems to be less about fruit and its countability and instead about the grammaticality, or perhaps the senses and referents, of the options you give.
All three options are grammatical, strictly speaking. However, their meanings differ slightly. If you're referring to a situation in which a child kicks a basket containing some oranges, the correct option of the three is the last one,
Groaning, the child kicked the basket of fruit away from her.
This last option is the only one that would refer to a basket containing pieces of fruit, all of which were oranges, and in which the focus of the sentence is the kicking of the basket as an expression of whatever the child is groaning about.
The other options do something slightly different. The second would refer to a basket containing more than one kind of fruit, as in this answer to the question I mention above. In reference to your comment on the second option, to indicate a basket containing only one orange you'd need to specify it with something like "the basket containing the piece of fruit". Your second option would be useful if your focus isn't the child's action but rather the basket or its contents—for example if you were trying to distinguish it from another basket containing something different or draw attention to the fact there was only a single orange in the basket.