Tension is your worst enemy when it comes to a fluid swing. Tension throughout the body is often the direct result of gripping the bat incorrectly. A player with a relaxed grip on the bat will be able to react faster and wait longer on a pitch than a player with a death grip on the bat. You want to be relaxed in the box; this starts when you pick up the bat.
You'll see various types of grips at all levels of baseball and you'll also read or see some people who believe there is only one way to grip the bat. If this was true you'd see all major league players using the same grip. The variables with the grip are how far out on the fingers or deep in the palm a player will hold the bat, how the upper and lower hands aligns on the bat, how tight to hold the bat, and whether to choke up or not.
With young players I will show them how to grip the bat and I start them out with middle knuckles approximately lined up and I try to get them to get the bat out of the palm and into the fingers where they will have better control (Image g1). Younger players have an easier time relaxing their hands when they don't have the bat buried in the palm of their hands. One quick way to check a player is to have him hold the bat out in front and look to see if there is a gap between the bat handle and the spot between the thumb and index finger (Image g3 below).
As players develop they will often adjust their grip and sometimes bring the grip back closer to the pad in one or both hands. The grip needs to be comfortable and it must provide the player with the ability to have a relaxed grip. Remember, tension is the enemy.
In the end you want players hands to align somewhere from the middle knuckles lining up (Image g1 below) and the middle knuckles of the lower hand lining up with the top knuckles on the upper hand (Image g2 below). Anywhere in that zone that is comfortable for the player should work as long as they don't get the bat too far in the palms of their hands.
The best answer is to grip it as firm as you'd like as long as the grip is relaxed. The grip has to allow a player to take a natural swing. In looking at the images below, Image g4 is the grip that jumps out and yells "fix me". In this grip the player has the bat buried in the palms of his hands and you can see the tension in the hands and the arms. The alignment of the knuckles will also inhibit his natural swing. One of the keys to having a quick bat is the ability for the top hand to snap the wrists forward just before contact. "Bat lag" is a term to describe the relationship of the bat head to the hands as the swing progresses towards contact. As the hands come forward into the zone the bat head which is trailing behind is whipped by the wrists forward to contact to generate a tremendous amount of bat speed. Bat lag is not to be confused with bat drag. Bad drag has a negative impact on the swing and is a common problem with young hitters. Bat drag is fairly easy to pick out as the hitter will look like he is having a difficult time getting the bat head to the ball and through the zone. It can be caused by a player using a bat that is too heavy and also by poor mechanics in general. Improper grip as shown in Image g4 can be one cause of bat drag because the grip inhibits the ability of the wrists to snap the bat forward. Gripping the bat too tight with a proper grip can also contribute to the bat drag.
Choking up is when a hitter will move his hands off the knob of the bat and place them higher on the bat where there will be handle showing between the knob and the bottom hand. Many young hitters don't want to try choking up on the bat and I believe their cheating themselves of a technique that can benefit their hitting in a number of situations. Two strike hitting is a perfect example of when choking up can be a real benefit. By choking up on the bat, you've effectively made it shorter and more balanced. This will give you better bat control and make you quicker. With two strikes this can help you stay alive by fouling off tough pitches that you may have missed otherwise. Another situation where choking up can help is against a pitcher that can really throw hard. If you're having a difficult time catching up to a fastball, choke up and stay relaxed. Often young players tense up when facing a fast pitcher and as a result make their reactions slower.
Remember relaxed muscles will react quicker than tense muscles. So if you want to have a quick bat, relax those hands which in turn will help you relax at the plate.