How do you "weed out" the good startups vs the "bad" ones? I get quite a few random emails / LinkedIn messages from Start Ups, but I am weary. Anyone know a way to do research on their company before replying?

google for article on how venture capitalists choose to invest in startups.
Most likely they don't invest in the idea of the founders. They invest because they believe in the people. How their attitude are. That needs a one on one talk.

For "startup" cold calls:

1. Are they established (website, news stories, press releases, first customer)?
2. Is their product anywhere at demonstrable MVP?
3. Do they have verifiably secured funding?
4. Are they competitive in their salary offering?
5. Are they offering relo or have a local office (red flag if no)?

Few other questions, but those are the big ones.

1-3, should have at least 2 of them.
4, should meet baseline salary++ before any options, pre-funding options might as well be toilet paper.
If 5 is no, bail on them, never take remote from a startup, especially if they're not in the same country.

Last one is to ascertain if they should be interested in you. Early stage startups hire mostly heavy hitters. If they're < 10 and looking to staff people without CV weight, that's a red flag.

You can't. If it would be possible, the capital they get wouldn't have "Venture" in its name.

Just join the one wich provides the most interesting projects and best work conditions.