The leverage they get from a non-partner handling operational stuff or due diligence isn’t terribly great, and almost certainly isn’t the same as helping to find the next great investment.
But because of how long this takes, it pays to invest time even with funds that don’t immediately seem like great prospects, as long as you think that they are on the rise and likely to expand their team over the next year or two.
Beyond that, I actually wouldn’t sweat some other things too much early in your career (stage, sectors, team size, etc)
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* If you are unable to get into VC now but want to later, I think a good path is to work at a winning, high growth company and make a great impact.