%STR will add STR based on a percentage of your (base STR+flat bonuses from equipment+MW bonus).

%ATK will add attack based on a percentage of your total attack, not counting any other % bonuses to attack.

+ATK will just add that flat amount of attack.

%Total Damage will add a percentage of your base damage range to your damage range. Base excludes other %total bonuses, whether from skills or equipment. %Boss Damage is just %Total Damage that applies only when attacking bosses.

As for which is best, it's situational. Consider the basic range formula, which for the high end of the damage range goes something like:

Weapon Multiplier * [4*(main stat) + (secondary stat)] * [Attack/Magic Attack depending on class]/100

Note: I may have gotten the specific numbers wrong but this is the gist of the damage formula.

If you have no % modifiers, adding 10% main stat will increase your damage by 10% (ignoring the effect of secondary stat, since it's very small compared to main stat). Similarly, adding 10% attack or 10% total damage will also increase your damage by 10%.

Notice that modifiers of the same type will be additive with each other. Say you have 10% main stat on two pieces of equipment. Then you get a 10%+10%=20% bonus to your main stat, so a 20% overall damage boost.

But notice that modifiers of different types will be multiplicative with each other. Say you have 10% main stat and 10% attack. Now the stat term in the formula and the attack term in the formula are each increased by a factor of 1.1. Then the total is increased by a factor of 1.1*1.1=1.21, giving a 21% boost. This, of course, is greater than the 20% boost of having 10% main and 10% main. The effect will naturally be greater with greater % bonuses. E.g. 50% main and 50% total gives a 2.25x multiplier, as opposed to a 2x multiplier from 100% main.

Stacking a lot of only one of %main stat, or %total, or %attack, will result in diminishing returns. But since they're all multiplicative with each other, stacking some of each will produce the best results, as their bonuses are multiplicative. Thus it really depends on what you've got a lot of. Some classes, for example archmages, have substantial %total built into their skills, which makes adding %total or even %boss from equipment less effective than it otherwise would be.

But in general, %attack is the hardest of these sort of stats to come by. Those potential lines appear only on weapons, secondary weapons, and emblems, so it's harder to get a lot. %STR can appear on anything, so it's relatively easy to get. %Total is on the same equipment types as %attack, but it's basically the same as %boss, which comes in much bigger percentages.

Since %attack is generally the hardest to get a lot of, as a rule of thumb, it's best to have %attack over %total or %STR on anything you can get it on. %boss may be better than %attack, just because of how much bigger the percentages you get per line are, but that depends on what you already have and what class you are.