You'll need a glove that fits your hand and skill level, and is geared to the position you play. There's a lot of truth to the old saying, "Fits like a glove" — if you're glove is too big, or small, you may have problems catching and fielding the ball. For beginners, gloves that are about 9 1⁄2 to 11 inches long are a good start.
You can't play without a bat and ball! Try aluminum or other non-wooden bats — they are lighter and easier to handle. As for the ball, you can find softballs at most stores that sell sports equipment.
Also, for organized team play, you'll need a pair of shoes with rubber cleats — they dig into the ground and can give you more traction while running the bases or fielding a ball. If you're playing a pick-up game with your friends, a pair of sneakers will do. If you're a catcher, you'll need special protective gear like a helmet with a facemask, shin guards, and a chest protector.
And remember, always wear a helmet to protect your head while at the plate, or on base!