Google and Bing have keyword tools that show the search volume on any keywords, or phrases that you type into them. If you intend to advertise on Bing, do not use the Google for your research because their search volume and user demographics are very different.
Note the geographical area that you are searching and make sure it matches the offer you intend on running. In other words, if you're looking at search volume in the USA but the offer is only valid in the UK, your numbers are going to be way off. Same deal if you've only selected USA and the product ships worldwide.
Usually you want to see a healthy amount of searches, like several hundred per day. There must be enough search volume to justify doing all the work and running the ad. (The exception being brand new products.)
At the moment, you're only concerned with the top volume phrases. Bid on those to start. Don't worry about long tail phrases. You can always add them later. At this point, you just want to see if the offer converts into sales.
As mentioned earlier, an exception to the low search volume rule are new items without any prior search history. Those can be worth setting up because lazy affiliates won't touch them, meaning no competition for you.
You never know, that new product might be on the launching pad for sky high profits. It could be featured on a TV program like Shark Tank, the focus of a daytime health show, endorsed in a celebrity talk show, or about to embark on a major TV, radio and print campaign.