There alot of things that will matter. Equipment isn't everything, but it sure does matter when you have honed your fundementals.
You do need a steady rest, one that doesn't influence the barrel. The type of rest you use depends on how you want to use the rifle. If you are going to be benching most of the time, I would get a nice front rest. Sinclair International has some nice ones, there are many other suppliers. You could go with a small pack or bag filled with any material that will hold it's shape, but still conform to the forend. If you want something that is always with the rifle, a good bipod is great. Harris is my favorite.
Depending on the type of rest used, they can affect accuracy. From my experience, the rifle needs to move in the rest. Meaning that during recoil, the rifle needs to "slide" otherwise, the recoil may cause the rifle to "torque" and this will matter some. Alot of benchrest shooters use teflon tape on the forend bottom and use baby powder on the front bags. Also, the newer bags have a seam sewn in, this limits the friction area, allowing free recoil.
I'm typically not "benching" my rifles, I like bipods. In my opinion, they are more usefull to me.
Your fundementals need to be consistent.
Body alignment, natural point of aim. Get straight behind the rifle. You should be comfortable behind the rifle in, once in position and sighted in, close your eyes and gently shake side to side, open your eyes and see where you are on the target. If you are no longer on target, adjust your position until you stay on after the drill. After time, you will know by feel what is right.
Firm grip and firm in the shoulder
Consistent cheek weld-no shadows in the scope. Make sure that your set up will allow you to get the proper eye relief and not make you strain to stay in position.
Stare at the cross hairs
Breathing, shoot on your normal respiratory pause. This is most consistent, if you try the half breath, quarter breath, whatever, it's not consistent at all. During your normal respiratory pause, apply smooth, steady pressure to the rear on the trigger.
Follow through!, meaning, keep doing everything you did before the shot slightly after th eshot. If you relax to soon, you influnce the shot by changing everything you did beforehand.
You do need good ammunition though, other wise you are beating your head against the wall try to obtain the accuracy you want.
Hopefully this helps, I'm sure there are other fine pointers inbound.
edit-as a general rule in relation to fundementals, vertical string is your breathing, horizontal, body alignment and triangle shaped ones are not staring at the crosshairs.
Mark