Whenever you're approaching a VC firm for funding, it's always optimal (surprise!) to connect with the partner in the firm who has the closest investment interest to the space your startup is going after. As busy as most good VC's are, it's usually hard to stop what one is doing and take time to come up to speed on a new market unless one is making a calculated shift in one's area of investment interest (which does happen --- over time).
No matter how hard you try as partner in a VC firm (and I have to say that, at Mayfield, I’m pleased at how hard we try), it’s difficult to be as interested in a deal passed along to you by a partner as you are in one that comes in directly through your network. A number of reasons, but it mostly comes down to the fact that most good VC's are pretty busy and – for a referred deal -- you don’t have the same “context” as you do for a deal that comes to you directly from someone you know.
Not to say that good things don’t happen. At Mayfield and some other firms, the partners do pretty readily pass around deals that seem more appropriate to the interests and backgrounds of other partners. For example, at Mayfield, we have done two deals this year that came in initially through me but ended up being “done” by other partners (who, BTW, are better suited for the companies than I would have been).
Despite the above advice, however, there is a caveat: it's definitely better to get a good personal introduction to any partner in a particular firm than to it is to merely approach the “right” partner out of the blue. For a whole variety of reasons, VC firms almost never seriously consider deals that come in “over the transom”.
So, whenever possible, do your homework on the partners in a particular firm, and try to get a personal introduction to the one whose background and investing interests seem to best fit your company. From an informational perspective, this is usually not hard to do. Most VC firms have good descriptions of their partners’ backgrounds and interests on their web sites, and you can also tell a lot about what a partner is interested in by looking at the deals they’ve done.