Slims

For what it's worth, I ALWAYS wear hard armor when shooting and moving with other people. I don't think body armor is a bad idea at all if you spend a lot of time training...even professionals sometimes screw up and accidentally shoot their buddy (of course they are immediately fired, but you get my point).

I agree with Crompsin, for your purposes I would get a simple plate carrier with MOLLE and a slick level IIIA vest that is EASILY concealable (or it will be a hassle and you will leave it at home rather than wear it). Paraclete makes a lot of good products and they have a solid reputation. Check out Diamond Back Tactical also, though they may not make concealable armor.

For your range-armor I would recommend buying some soft inserts for your plate carrier (in addition to the plates, of course) and just running a plate carrier (or buy stand alone plates, which are more expensive but better). The soft armor on the sides won't protect your from a rifle around anyways, so don't bother with it.
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Oh, by the way, I am friends with one of the owners of Grey Group (the store whose pic you linked). Feel free to call them and ask your questions, they are a major paraclete dealer now and may have access to more than is up on the website.

They also run/coordinate a lot of good schools if you are seriously interested in practical shooting.

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