Help in writing patent claims

Hi
This it the first time a write a patent application. I have question on writing the claims. I read a book that tell me to write a few independent claims by trying to look at the invention at different angles. I am planning to write one as a complete system, one as Jepson style and one as Method claim. Below is an example:

There is a product A that is very common and a lot of manfacturer making it, it perform a function but it has an unwanted side effect. I invent a means B that eliminates the unwanted side effect.
1) First independent claim is a system comprises of A and B that can produce the desire result but without the unwanted side effect.
2) Second independent Jepson style that the embodiment comprises of B alone and the embodiment is to be add onto the common product A to get rid of the unwanted side effect.
3) Third independent claim is a Method claim of steps of method to get rid of the unwanted side effect by steps using means inside B.

I just want to get some feedback on what I am doing.

Thank

Alan