If the cryptanalyst happens to know the plaintext behind a cryptogram, he will be able to retrieve the plaintext behind every cryptogram encrypted with the same key stream. Also, knowledge of the period allows a cryptanalyst to add two cryptograms and achieve some results concerning the two added plaintexts. A long period means that repetition will not occur in practice. The length of the linear equivalent defines how many cryptogram bits with known plaintext that are required for direct generation of the key stream hiding the rest of the plaintext. Of course this number should also be as large as possible.
Less balance means better chances at guessing.
A primitive polynomial gives a perfect balance except for a slight unavoidable imbalance for the all-zero subsequences. 2 n -1, where n is the degree of the polynomial. Points are obviously given for correct answers to the question that did appear in the text. If you XOR the output of three polynomials you get a linear equivalent with a feedback polynomial that is the product of the LFSRs generating the XORed sequencens. Its balance is just as close to perfect as the added sequences.