Perhaps the first thing to note is that, like the Justice she will be replacing, Justice Souter, she is a bit of a stealth judge. She hasn't decided any monumentally controversial cases. As with Justice Souter, it will be difficult to predict how she will decide controversial cases that come before the Supreme Court on the basis of her past judgments.
This is because she was an appeals court judge in the Second Circuit. The Second Circuit includes New York, Connecticut and Vermont. The hot button issues tend to be litigated in states that are challenging controversial precedents -- abortion, prayer in school, death penalty and so on.
The legislators and public officials of New York, New Connecticut and Vermont generally don't try to limit abortion or place granite sculptures of the Ten Commandments in public places. None of the Second Circuit states have attempted to execute anyone, so she's never decided a death penalty case.
Her only controversial decision was in the New Haven firefighters' case, but she didn't write the opinion.
So what kinds of cases have come up to Judge Sotomayor in the Second Circuit? Lots of criminal procedure and immigration cases. I'm sure that many securities and financial cases have come before her, but these are not likely to be understood by the general public, let alone rile up the general public.
Most of the opinions she has written that have been summarized by the Supreme Court blog (Scotusblog) are about the minutia of criminal procedure and of immigration procedure.
The only thing one can conclude from the record of her opinions is that she has not tried to "make law" from the bench and has scrupulously followed precedent in highly technical procedural cases. Her participation in the New Haven decision, her background, and her experience as both a prosecutor and trial judge, suggest, however, that she will be in favor of affirmative action, and that she will support procedural rights of criminal defendants. She is by all accounts a terrifically nice, sociable person, and some commentators have speculated that her most important "audience" is Justice Kennedy, the swing judge; her sociability will help in bringing Justice Kennedy around on controversial cases. She is also a voluble questioner during oral arguments before the appeals court.
It will be difficult for the Republicans to "paint" her as anything in particular, in terms of judicial approach.
You can read summaries of her major opinions at the Scotusblog, here:
http://www.scotusblog.com/wp/judge-sotomayor%E2%80%99s-opinions-with-dissents-%E2%80%93-part-i/