Niche - choose something that you know a little bit about, or at least is interesting to you. Do you gamble?
Do you like iPhones? Do you have any experience with payday loans?
If you can get in the heads of the target audience and know their wants and desires, then that would be a good fit for you. Don't try to promote an Android phone giveaway if you can't even list some bullet points about why the new android phone is better. Promote something that you use, and have knowledge about.
Then, there's the traffic. How do you plan to put the offer in front of a converting audience? I would suggest you check the offer. Each one has different allowed types of traffic, so this really can't be answered here in full.
What offers are you wanting to promote?