Adding category to user registration and display profile (categorised) frontend

I am not sure about it as i have seen som many of the similar queries here but none seems to solve my requirement. i didn’t find plugin for it or may be i am not hitting the right keys to get it. Please help me out…

My requirement is:

to create member directory where members can opt for category say (Chemistry teacher / Physic lecturer etc)
he/she register from frontend with some fields say (Name, email, phone number, category[as mentioned above] and a brief profile with profile picture).

Now this listing i would like to be list out categorised on page and the listings to be searchable.

if you are aware of any such plugin or something please suggest me.

Thanks in advance.

Kautuk