Whats the best way to start out pushing those offers? POF and Facebook are out of the question. Prepared to spend $2k+ for trial and error.
PPV? Media Buys? Adult ?
Point me in a direction 
Traffic Junky + Muscle offer worth a try? Not asking for a campaign on a silver plate but some general direction would be great 
When I ran those niches in the US (I presume you mean the US?) it was via media buys. And you can expect to spend a good deal more than $2k on media buys to get a campaign working well in such established niches as these. It's significantly cheaper to do it in clever ways via FB in my opinion.
Best bet is to test out international countries.
I'm very good at promoting intl. health offers, can you guys suggest a network or some networks that got such offers?
You could go international which is recommended, sure, or you could find Americans where budget/money isn't a concern at all... often the EPC makes up for it and the sale is much easier.
We have several in a lot of verticals
For US Display traffic there's only one word you need to know: Yabuka. If you see the slots they're buying, it's all health/general web traffic, they have astounding reach and reasonable prices too. No I don't work for them, lol. $1k min dep.