The ranking of most hands is the same as in Poker except you are using only three cards and a straight is higher than a flush. So a mini-royal flush (AKQ) and straight flush are at the top of the hand rankings, followed by three of a kind, straight, flush, pair, and high card.
Since there are no community cards or shared cards of any kind in 3-card poker, the strategy is somewhat straightforward. The complete average hand in 3-card poker is queen-6-4. Therefore, the optimal strategy would be to play all hands greater than or equal to queen-6-4, and fold all hands worse.