A microphone for recording conversations

Sorry, it's not going to work.

Microphones are all about proximity; the closer the mic is to the sound source the less other noise will be picked up by the mic, the further away the mic is from the sound source the more ambient noise will be picked up by the mic.

Mics also need to be aimed properly. Being off-axis just a little bit can reduce pick-up or/and alter the tonal quality of the sound significantly.

Your best option - assuming that you want the mic hidden - would be a lavalier mic. Lavs are (relatively) small so can be hidden fairly easily; quality lavs can be incredibly small, and quite expensive. The placement of lavs on clothing will take some experimentation so the wire is not strained and you don't get "rubs." You are also going to need an audio recorder.

With your budget you will end up with passable consumer "toys." Perhaps something like this for the lav:

http://www.bhphotovideo.com/c/product/1024938-REG/polsen_pl_5_mini_omni_lavalier.html

And this for the recorder:

http://www.bhphotovideo.com/c/product/757065-REG/Tascam_DR_05_DR_05_Portable_Handheld_Digital.html

That keeps you close to your budget. You can do your own research now that you know what to look for.

You should also get some lav mounting supplies. Experiment with placement.

That's the best I've got for you. The sound quality will be fair to good, the pick-up of your interviewees (or what ever they are) will be poor to fair and possibly decent depending upon conditions.