Facebook Ads: Tactics For Likes

So I've been trying to grow a new fanpage using FB sidebar ads.
I'm targeting likes from just USA, and potential audience is 30million (all interested in specific niche).

I've tested out 3 different ad copy/image with CTR ranging from 0.1% to 1.4%.
Average cost per like is around the 27 cents mark, which is pretty high.

Looking for some pointers - what have you found to be the cheapest way to get likes using FB ads?

Is it better to target big audience or small?
Do you find CPM/Optimized CPM cheaper than CPC?
Whats your daily budget?

When I ran optimized CPM with a $5 daily budget average cost per like was 27cents (over 10 days).
When I tried CPC for the exact same ads, suggested bid was 75cents to $1. I set max bid to 25cents and as a result they've had a tiny reach (no likes). Am I better of just setting max bid in the recommended range and hoping price drops?
Or am I missing something here - surely this is way to costly to grow a fan page? I've sent traffic to landing pages for far cheaper than this...

And while I'm at it, why is it that my Cost Per Like is higher for an ad with a higher CTR? What the hell, Facebook?!!

Appreciate any help or tips you could give.

Thanks!

I don't have any pointers, I'm just curious: Why are you still investing into fb pages? Most people have less and less success with them, is it for a business or something?

Not grown a fan page properly before so I'm interested to test it out for myself.
Not too worried about people saying success is less and less. I see it like this - there's an opportunity on FB to engage with demographic who are interested in what you're putting out there. Sure, the potential audience might be less than it was a year or two ago, and it might be harder to get your content on their feeds, but an audience is an audience. You're a marketer. If you're clever, there's lots of ways to monetize a passionate group of people.