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The Golden Thread shop has an item called "Costume Selective Enhancement" that allows you to +1 upgrade a costume by spending 1600 Golden Thread. It is available to buy once a month.
This is a far more effective way of getting dupes of costumes than pulling on the select banner, which has really low rates of getting the costume you want.
You cannot use the "Costume Selective Enhancement" to +1 limited costumes, or newly released costumes whilst their featured banner is running.
This guide sets out some recommended units to spend on.
Adventurer Diana
Adventurer of the Unknown Diana is the best supporter in the game. Having her at +5 is necessary to complete a lot of end-game content. Although she only works for on-element attackers, this is not as niche as you might think: for end-game content, you are almost always using on-element attackers to maximize damage.
She is therefore recommended as universally useful unit to get to +5.
Homunculus Lathel and B-Rank Helena
H.Lathel and B.Helena are the best 5-star physical and magic supporters, respectively.
For H.Lathel, getting him to +3 is recommended for physical teams, especially for use in PVP. The power boosts at +4 and +5 are relatively small.
For B.Helena, there are big power boosts to her buff at +4 and +5.
Whenever a costume appears in the featured banner, there will be a "Costume Pickup" event which rewards you with 10 draw tickets for every copy of the costume you own (from +0 to +4). Note that getting a costume to +5 rewards you with Ancient Crystals from the "Costume Pickup" event instead of draw tickets.
You cannot use "Costume Selective Enhancement" to +1 newly released units. However, if you use "Costume Selective Enhancement" to +1 a costume that is currently on a re-run banner, you will be rewarded with 10 draw tickets from the "Costume Pickup" event. This is a great way to get extra value out of your Golden Thread spend.
Pool Party Angelica (for PVE)
Pool Party Angelica is a great all rounder in PVE, thanks to her massive damage against strong opponents. At +5, allowing for chain damage, Angelica's damage is (0.25 + 0.25 x 1.1 + 0.25 x 1.2) x Max HP of the target. Simplified, that means 82.5% x Max HP of the target before crit.
However, the "Max HP" part of the equation is capped at 20,000 HP. This means that without crit, Angelica's max damage against an enemy with 20,000HP or more is 82.5% x 20,000 = 16,500 magic damage.
Unlike most units that have a base crit dmg of 50%, Angelica's base crit dmg is 100%. She also has a unique weapon which increases her crit damage by 90% at UR level, so it's easier to reach high crit dmg. For example at 400% crit dmg with crit on all 3 hits against an enemy with 20,000HP or more, Angelica would deal 82,500 magic damage.
With both excellent damage and 4-tile AOE, she is a universally useful costume that will help you clear tough PVE content. Her main downside is that her damage potential is capped because she does not benefit from M.ATK supporters. She is also best played with supporters who can buff her crit rate.
White Cat Rou (for PVP)
If you have White Cat Rou at +1 or +2, getting her to +3 is a worthwhile investment for PVP play. At +3, White Cat Rou costs only 1 SP, making her easy to slot into any team. She has a reasonable chance at dealing lethal damage with her knockback, and then on your opponent's turn she is a tank that is very hard to kill with her evasion ability. White Cat Rou has consistently been rated top tier for PVP since launch.
Your favorite 5-star costume
Finally, if there is a 5-star costume that you use often, by all means upgrade it.
Note that most costumes have their SP cost reduced at +1 or +3. The SP cost reduction makes a big difference (especially in PVP), so also consider which units you need to have the SP cost reduction the most.