The most neutral-sounding sentence would be:
[私]{わたし}は [公園]{こうえん}で さくらに ボールを [投]{な}げる。
Watashi wa kōen de Sakura ni bōru o nageru.
私 being the topicalized subject, this sentence states what the speaker will do. No particular emphasis is placed on any part of it, although, depending on the context or the way it is said, the sentence may put what the speaker will do in contrast to what other people will do.
The subject marker が needs to be restored when the topic marker は is removed. In other words, when a subject is topicalized, が is replaced with は.
私が 公園で さくらに ボールを 投げる。
Watashi ga kōen de Sakura ni bōru o nageru.
This sentence emphasizes the fact that it is the speaker, not other people, who will throw a ball to Sakura in the park.
Other parts of the sentence may be taken out as the topic and moved up to the top, but you need to be careful what to do with the original particle.
When what is marked with を is topicalized, を is replaced with は, just like が is.
ボールは 私が 公園で さくらに 投げる。
Bōru wa watashi ga kōen de Sakura ni nageru.
This sentence talks about what will happen to the ball, which is promoted as a common topic between the speaker and the listener. The listener is expected to already know what ball is referred to. As the speaker, when you have to single out the ball as the topic like that, you most probably have something else in mind with which you specifically put the ball into contrast. For example, you or someone else might take some other action with a bat or a glove, but as far as the ball is concerned, you will throw it to Sakura in the park.
Other particles are usually retained, and は is added after them, when what is marked with them is topicalized.
公園では 私が さくらに ボールを 投げる。
Kōen dewa watashi ga Sakura ni bōru o nageru.
This sentence talks about what will happen in the park, which is singled out as the topic as opposed to other places. Some other action might be taken in those other places, but if you limit the place to the park, you will throw a ball to Sakura there.
さくらには 私が 公園で ボールを 投げる。
Sakura niwa watashi ga kōen de bōru o nageru.
This sentence talks about what will be done to Sakura. Other people might become targets of some other action, but as for Sakura, you will throw a ball to her in the park.
に is practically mandatory in the last sentence above because, without it, what function さくら plays in the sentence would be unclear. In fact, removing に from the original sentence would result in a sentence that doesn't make sense (if not understood differently).
私が 公園で さくら ボールを 投げる。
Watashi ga kōen de Sakura bōru o nageru.
However, this is not always the case. The following three sentences are all understood as meaning the same: you may not go to other places but you do go to the park.
公園には 行く。
Kōen niwa iku.
公園へは 行く。
Kōen ewa iku.
公園は 行く。
Kōen wa iku.
The reason に or へ is optional in this case is that, 行く being a motion verb that typically requires a destination, 公園 is understood as indicating that even if it is not marked with に or へ. Though not quite grammatical, the following sentence is at least unambiguous.
公園 行く。
Kōen iku.
