IMHO, local government is the one that matters most, because your vote has the most sway.
Hopefully you have a functional, if barebones, local newspaper, that reports on at least some of the happenings of city council / county board meetings / etc local boards. Combine that with candidate statements (when present, but know that candidates have to pay per word to put those in --- to pay for translation and printing costs). My criteria are 1) does this person appear to make rational decisions and learn from experience. (Are they providing effective and honest government) 2) Does this person tend to make decisions I would like. Usually, I would pick a rational person over a person who does things all over the place but often in directions I prefer --- but not if the effective agent is specifically against my interests.
I look for specificity in candiate statements, but will not vote for candidates who promise things outside the baliwick of office (ex: mayoral candidates promising to fix schools; when schools are generally controlled by a school board, not the apparatus of city government), or unreasonable things (government moves too slowly: open meeting laws require significant advance notice of proposed action - a local elected official can't (shouldn't) do things quickly and promising to do so implies significant misunderstanding of the workings).
For propositions, I read the submitted statements, and the 'non partisan' summary by the election personell, and sometimes the actual text. I try to consider the difference between the intent and the text, and if the text will be effective. In CA especially, I also consider how much of a pain it will be in 10-50 years when it's obsolete but hard to get rid of; and if this is a good idea, why couldn't it get passed as a regular law. In WA, it's less critical, because the state supreme court blocks or makes ineffective a lot of propositions if they feel it addresses something that is the proper job of the legislature.
I abstain from non-binding advisory votes, unless they're on a topic I care deeply about, because I feel they're insulting. For examlple, by WA proposition, we have to see an advisory vote on new taxes, but it's meaningless; the proposition specified the votes were binding, but the supreme court ruled that taxes are the job of legislature, and the people can't usurp it. I would vote to repeal the now useless proposition.