As you say, away teams are picked based on the expertise of members of the senior staff. Data would be science, JordiGeordi engineering, Crusher medical, Troi for diplomatic things, Worf/Tasha for security, with Riker commanding.
As for the unknown worlds part, most weren't unknown, as far as I remember. Most of the stuff they did was within Federation space. Those that were unknown at the very least had some known about them, enough to determine who to send down. Most Star Trek stuff isn't so much about exploring unknown worlds. In TNG it's mostly diplomatic.