I have both - fixed power and variables. A higher powered scope will give you smaller groups...if you have a rock solid rest. But not by a whole lot. True bench rest guns have fixed power scopes on them. Usually 24X to 36X. This is way too much power for any thing except bench rest work. I have shot black birds with a fixed 10X at about 250 yards. I am talking about a target that is less than 2.5" across at the chest. I had to "walk" the shot in. It took three shots on the first bird and 2 on the second bird. There was a cross wind and I was estimating the distance with a 222 Remington. I could see the bird "duck" and knew I was getting close. The point is I could see the target just fine with a 10X scope. Unless you get a very good scope, your point of aim will change slightly when you turn the power up or down. If you can put your cross hair on a target and still see the target, you have enough power to shoot accurately. I do not know what sized targets you are planning on shooting at 300 yards, but if it is a 3" Bullseye or so, you will have no trouble seeing it with a 10X as long as it has fine enough cross hairs.
Here is a picture of a target I shot at 100 yards with a 6.5X - 20X variable. I was trying to see if the point of impact changed from one power setting to another. There were slight changes. Another reason I think fixed powers are more accurate over all. But you can see that there is not a whole lot of difference in the group size from 12X to 20X. More than one group at each setting would have to be fired to really prove that out.
I have a Bushnell 3200 Elite 10X. It is a pretty good scope for the money. It has mil-dots; the elevation and windage adjustments seem very repeatable. They are ruggedly built.
I am presently building a 223 for some long distance shooting, but at PD, not fixed targets. It is going to be very heavy, around 14-15 pounds when finished. I have planned on purchasing another Bushnell 3200 Elite 10X for this rig. I just saw a Nikon on sale for $300 that looks interesting. Both have mil-dots, both have target knobs, but the Nikon has a side AO and comes with a sun shade. On the down side the Nikon is a variable, but I can set it at 10X and do all my shooting at that power range and I do not have first hand knowledge to know how rugged it is or repeatable the setting are. I think I am still going to get the Bushnell...but. Good Luck and Good Shooting
One more thing, check the prices at Mid South Shooters Supply. I buy from both, but find in many cases that Mid South is cheaper if both have the same product.