SHA-1 is weak, but not fully broken. SHA-256 is just an extension to SHA-1, currently it's probably also weaker than first thought (given the same weakness is thought to affect the whole sha family), however it still requires a lot of computing power to get a match.
Anyway, in terms of digital signatures, this becomes less of a problem due to the way that's just the final step. There is still encryption first.
As for key size whether RSA or ElGammel/DSA I would recommend 2048 bit keys anyway now.
the difference is RSA is based on factorial math while ElGammel/DSA is based on logarithmic math, neither can necessarily be considered better or worse (to not though i that elliptic curve based stuff is closely related to the logarithms stuff).