GSSR (Knights or Cavalry)

It’s hard to say really. As you said before, Knights has Arjuna and Karna who excel in their classes and would certainly break ground for your weaknesses. That being said, most of the other SSRs in the Knight banner are quite average in their respective classes.

Cavalry has top quality servants for sure, but it sounds like you’d have a high risk for duplicates or redundancies rolling from that banner as well.

I personally favor the Knight banner mostly because of the off chance of getting Arjuna would allow me to switch out Emiya as my go to Archer. Karna is great as well for someone missing a Lancer. I use Brynhild so he’s not nearly as much of a priority despite being the best Lancer in the US game

But that’s really the only upside I can think of for the Knight banner. I personally go more for a safe returns over high risk situations though

Well I will try to list the pros oof what I feel would be good for you in each banner. Biggest draw I feel would be Cu Alter, Waver, Ozymandias < These require little explanation other than they are the best at what they do. CU berserker with the survivability of a cockroach and high base stats and powerful NP even without buffs. Waver broken support one size fits all teams. Ozy best rider has Dio Brando voice and the most insane offensive skillset in his class. Tamamo is the Definitive Arts Servant Cornerstone she will get interludes and animation updates in the future too(if you roll on the summer banner after getting her you can build the Samosan Moedred Rider System/ Also works with Artoria Archer)
Meh Servants
1. Vlad (Arts Zerker) not that strong without tamamo broken if you have her
2. Drake good farmer and all rounder just got powercrept by newer servants
3. Xuanzang has big assets, fills assassin killer niche still useful in certain scenarios
4. Nightingale support zerker that can debuff the fck out of the enemy
The Bad( for you at least)
NP2 Jack
Mebd

Knights
Artoria (Bad), Altera and Mordred (Decent)
All good farmers with Altera being able to dish out more damage while Mordred having the advantage of having a NP charge ability. Artoria might get a costume buff in the future since rumors are flying around but not likely.
Orion (Bad)
Low attack stat for an archer. Kit centers around anti male servants. Bad NP gain and weak outside of arts teams.
Tesla (Great)
Strong archer and will become a top tier once they buff his chance to 100% on Pioneer of the stars skill. Still a great pickup and is comparable(but not quite there) to Gilgamesh.
Arjuna(Decent)
Aoe Archer good stats and NP gain but lacks anything special outside of farming
Karna(Great)
Strong Lancer great skillset and will fit into most teams you put him into
Jeanne(Bad to Great)
Once she gets her NP interlude she will be a staple in Challenge quests and be very strong. But thats also her demerit she will only be useful for the harder and gimmicky content and not much else. Also requires expensive investment for skill and ascension materials.

Cavalry
3 Amazing Servants that are good for you
4 meh
2 Really bad
Knights
2 Bad
3 Decent
2 Great
1 Debatable Bad to Great

If we take a look at the remaining year's free servants, we have an assassin archer saber lancer. You need to fill the st lancer slot, meaning you actually do not benefit much from the knight banner. Unless you roll ruler. From cavalry, pulling drake ozy zhuge xuanzang are good for you. Pull on cavalry and roll for kiyo or tamamo lancer in summer banner.
Pull for what you need. None of the knights fulfill your needs well esp since we get a free archer soon