Character Build: Make a (socially) Interesting Character

Well, you don't have to go this far.

So, you might say there is kind of a spectrum of GMing styles ranging from "I want my players to experience an awesome story", or more pejoratively, "railroad," and at the other end, you have, "I want to give my player all the tools and freedom they need to enjoy themselves however they want" or more pejoratively, "sandbox."
I kinda start closer to the sandbox end to flush out what my players are looking for, and when they hone in on it, I start filling in the details around the point of interest they choose. This means I react to what the players want to do by accommodating the things they work towards. In a pseudo-meta way, if the world shapes itself to what it looks like my players want.
Therefore, the only way something just "happens" to a player is:

• It is the natural consequence of something the player has done
• The player has spent points on something that catalyzes an interaction, (advantages with an appearance roll, or an enemy disadvantage)

So, let's dissect the second bullet point further, and see how we can have NPCs find a player character interesting enough to just go out of their way and talk to them.

Advantages

I tried to stick to this book
mainly.

First let's take a look at advantages that can make someone really cool. Now, the thing to separate here is that we are not (necessarily) talking about making this character a suave devil that can just go up and talk to strangers. We want the opposite. We want strangers to just come up and start talking to a suave devil. So let's see what we can do with the Basic Set.

• Reputation (p.26) By building a reputation with a particular group of people, members of that group will consider it an honor to have a chat with you. Whether the respect is in the form of quiet reverence, or in the form of hellos and how-do-you-dos as you walk down the street depends on letting the GM know how you want it to be handled.
• Rank (p.29) Rank gives you certain responsibilities in return for the advantages it gives you, so you can expect to interact with direct reports and those that are ranked above you. This is often represented by a Duty disadvantage if it is more extreme than a "quirk" level obligation.
• Allies (p.36) most specifically, but sometimes Contact Group or Contacts (p.44) can be used to have friends that need to interact with your character. Similarly a Favor (p.55) is a one shot friend!
• Patrons (p.72) can give you a kind superior who helps you from time to time, and depending on the type of relationship, it can include regular contact.
• Social Regard (p.86) means that people respect you for the groups you belong to, and can work similar to Reputation.
• Honest Face (p.101) means that some strangers will inherently confide in you just because you look trustworthy.

...But I added some stuff from
here too.

Additionally, the following from Social Engineering may help:

• Classic Features (p.78) can get you extra positive attention from a small group.
• Sexy Pose (p.78) can make people approach you, but still requires the player to make an initiative.
• Social Arbiter (p.79) can have colleagues search you out for advice.

Disadvantages

A lot of disadvantages also garner social interactions, but usually more in a context of conflict.

• Mistaken Identity (p.21) means that people you don't know will be coming up to you repeatedly in response to the actions of an unknown stranger. This is a good plot device for your GM if you don't mind getting roped into whatever nonsense the other version of you is wrapped up in
• A bad Reputation,(p.26) can potentially lead to harassment.
• Some compulsions (p.128) like Compulsive Generosity can lead to NPCs asking you for favors, knowing you will oblige.
• Dependants (p.131) obligates you to keeping someone safe and happy. Because you are responsible, in some degree, for their needs, they will need to ask you for help.
• Duty (p.133) the other side of the Rank advantage usually means a professional obligation to help direct reports, and to follow directions of superiors.
• Enemies (p.135) are kind of like the opposite of an Ally, but so are Dependants. Having an enemy means that you will be actively antagonized from time to time.
• A Secret (p.152) can help you get blackmailed if you are into negative attention.

Other Thoughts and Closing

I think just going out and getting yourself some might be the easier way, but the rules are tools meant to assist in defining a character and shape expectations. If you want to interact with people, but it would be easier, or make more sense for your character concept, for someone to approach you rather than you approach them, then these might all help. Unfortunately, acquiring these in play can be anywhere from difficult (forging a relationship strong enough to codify it as an Ally) to impossible (suddenly acquiring Classic Features) but are often fair game during character creation.