For the Special talent, you want +8.5% Thermal Damage
For basic stats you want +10.0% ATK. For the other stat you have three real options:
Alignment Index - Alignment Index gives the full squad more dmg dealt to Burning targets.
Given that 106 Alignment Index is only 1.06% extra damage dealt, even a maxed Alignment Index roll is not a huge percentage increase.
Skill Haste - Little Sunshine's Support Skill has a 10s duration and a 15s cooldown, so Skill Haste is useful to increase the uptime on her support skill.
With enough Skill Haste, Fritia can use her support skill every 10s, giving it 100% uptime.
S-Energy Regen - All operatives naturally regen 1 S-Energy per second. Fritia's Support skill uses 15 S-Energy and has a 15s cooldown, so she's normally fine.
If Fritia gets Skill Haste though then she will use her Support Skill more often than every 15s, meaning she is using more energy than she regens.
Thus if Fritia has some extra Skill Haste then S-Energy is useful for allowing her to use her support skill even for longer fights.
Note that her ideal weapon Strawberry Shortcake can maintain 100% uptime even without any extra Skill Haste.
It will take Little Sunshine 80 seconds of spamming her support skill every 10s with no extra S-Energy regen to have her support skill buff run out and not have the S-Energy to be able to re-apply it.
Very few enemies in SCZ take 80 seconds, and if you've got to the point you have a logistics officer you are considering re-rolling, I doubt any fight lasts that long for you.
Realistically the only fights that take that long are Neural Sim and Supreme Battleground bosses.
As such, you can generally get away with Little Sunshine not having any extra S-Energy regen, although it's not a bad roll to get.
Some maths:
Skill Haste formula:
Skill Haste works as a CD/(1+X) modifier.
A max Skill Haste roll is 19.3.
19.3 Skill Haste = 83.8% of normal cooldown
38.6 Skill Haste = 72.15% of normal cooldown
57.9 Skill Haste = 63.33% of normal cooldown
Since Fritia has 66% uptime already, she needs to reduce her cd by 33% in order to have 100% uptime on her buff.
Two maxed-roll Skill Haste buffs will give her support skill a cd of 10.82 seconds, which is generally all she needs in practice.
My recommendation for stats is thus two Skill Haste rolls.
For your third roll you can take:
S-Energy regen if fights consistently last a long time for you (around 2 minutes or more)
Alignment Index for just a bit more damage. Fritia won't quite have 100% uptime, but she'll be pretty close.
Skill Haste if you want Fritia to have max uptime on her buff. This is the highest-damage option.
If you do get three Skill Haste rolls then you don't need to max them - she just needs her Skill Haste rolls to add up to about 50 or more - Three 16.4 rolls is fine.
Given that Little Sunshine is a 4* operative, I don't recommend you use logistics re-rolls on her, but if you did those would be your options.
As for which squad to use, you will ideally want to use either Twilight or Amarna.
Twilight gives a nice resistance debuff for 5s on using her support skill, whereas Amarna gives a nice ballistic buff for 15s and an ATK buff for 1.5s upon her support skill dealing damage.
Which of these is more useful depends on what you are fighting and what other sources of resistance reduction and damage you have, as well as how much Skill Haste Fritia has.
(Given that Twilight only lasts 5s, it only has at-best 50% uptime, or 33% uptime if Fritia doesn't have any Skill Haste rolls)
In practice you might want to simply pick whichever of the two you find easier to acquire and use that - as you'll likely transfer the logistics squad from Little Sunshine over to a 5* support operative who can use it when you gain such an operative.
Since both Amarna and Twilight are both viable for some 5* support operative at endgame, both are fine for this purpose.
As such, don't worry too much about which logistics squad Fritia uses - you'll probably end up swapping them out later anyway.
Similarly, it's not worth re-rolling Little Sunshines logistics stats - those re-rolls are better used on 5* operatives.
If you are using Little Sunshine as a support because you don't have any better 5* supports or much investment into your other operatives, then you are likely not going to have much resistance reduction, in which case Twilight is likely better.
If you do have several good operatives or just lots of investment into your 4*'s, then Amarna is likely the better logistics squad for Little Sunshine, and is what I'd consider her ideal endgame set, but Twilight is still great if you already have it and want to just keep using that.