Affiliate Marketing Secrets

I have a e-commerce site and I would like to expand my social media campaigns.
With twitter, I find it relatively easy – it’s casual, a lot of random people talk to other random people, and each message is so transitory that I feel fine approaching people. (Not ‘selling’ per se, but saying hi or something)
With facebook, I feel like a spammer when I approach a stranger, even when he/she is obviously interested in my niche. I hate cold calling and I feel like one of those cold callers when I approach unknown people on facebook.
It’s especially hard because we’re not a big company known by everybody, and I also don’t have a huge budget with which I can run continuous facebook ads and/or ‘like us and get free stuff’ campaigns.
So my question is: how do people approach potential customers on facebook without being a spammer or spending too much money on it?
Is there a smart way to manage your facebook ad budget?
It is a very general question indeed, but any helpful comments would be appreciated.