The only frags you want to farm in shops are those worth 10 points in fragment refining once you get them to 5 stars.
Hinata
Shikamaru
Lee
Kabuto (You should get him anyway for utility purposes, If you're up to date on power for your level survival is easy)
Anko
Kankuro
Chouji

And then spend most of your stamina sweeping elites, there is a pattern to it. Every day you are guaranteed *atleast* 1 fragment on either your 1st, 2nd, or 3rd sweep of all elite instances that day, that isn't to say you can't get fragments from all 3 sweeps of an instance but only 1 will be a 100% drop rate.

How to be more efficient at sweeping Elite Instances

1. Sweep an instance 1 time, did you get a fragment? Yes/No
1a. If Yes move to Step 2
1b. If No, sweep it 1 more time, did you get a fragment? Yes/No
1c. If Yes move on to Step 2
1d. If No again, then you've confirmed that for today you're only "guaranteed" a fragment on the 3rd sweep

2. If you got a fragment on your first sweep, move on to another Instance of a character of your choosing and do 1 sweep, If you get a fragment again then sweep Another instance again to see if you will again get a fragment on the first sweep.

At this point you should be starting to understand, you'll quickly come to figure out which sweep will guarantee you a fragment that day.

Ideally, you want a guaranteed fragment on the 1st sweep of all instances so then you can sweep as many of them as possible and gain a good 30/40 fragments total for different characters from sweeping all elites one time with no stamina wasted.

In my experience, the number of days each week you're guaranteed a fragment on the first sweep heavily varies by account and possibly changes each week, I've heard of people having guaranteed 1st sweep fragments 4 or 5 days in a row.

For me, alot of my days are 2nd sweep guaranteed, which isn't as efficient, but still good enough for farming as you usually have a decent chance of getting a fragment on the 1st sweep as well.

Unless you are like right on the verge of upgrading a certain character, I can't recommend farming fragments on days that are 3rd sweep guaranteed, you waste so much stamina for little to no return, at that point you're better off farming awakening/gear materials you're running low on.

I hope all this helps.