Do you choose a target with Teemo Strategist before revealing cards to determine the damage?

Yes, you choose the target before revealing cards.

When Teemo, Strategist's "When I defend" trigger goes on the Chain, you choose the target enemy unit at that battlefield as part of putting the trigger on the Chain. Only after that does your opponent get a chance to react. When the ability resolves, you reveal the top 5 cards, count how many have Hidden, deal that much damage to the already-chosen target, then recycle all revealed cards.

This is consistent with Rule 355.5.b — triggered ability targets are chosen when the trigger goes on the Chain, not during resolution. (FAQs #7962, #914, #7592)