I follow certain criteria before picking the best affiliate programs. First thing I do is go through certain reviews of the program to know more about the conversions of the product. Secondly I check whether the program fits my temperament. Finally I would see what are the payment methods for the program.
None. I make my own sites so THEY don't tell me how to promote, THEY can't shut me down and THEY don't take most of the money
If it is a Clickbank product, then it is easier to assess. Go for products with at least 1) minimum gravity of 30 2) minimum payment for affiliate - $17
You should only think about if you can make quick cash out of it? If not, don't even look at it. All other things follow after this first thing. If you go for clickbank, you have many websites to help with other criteria like cbengine, cb-analytics etc. If you go for CJ, then check if the site is not new. Many new sites don't give commission for the sales you made. Find out suitable banner or text. Also if you are promoting through adwords, check that the site allows the keywords you like to use. Thus the list will be never ending as times go on.
I have a few things I look at. Competition is not a problem as the people above said. I think it's a good thing. Just do it better and it won't be an issue for you. Frequency of payment, payment amount, reputation of provider are the main things I look at. It has to make sense money wise obviously, but if it's something you are familier with or want to dive into then that would also be a big plus.
The criteria to pick your affiliate program would be amount of commission, reputable and fast payout and excellent product quality