How competitive do you want to be for 3-star tournaments? If you aim to just get top 50% I’d say you can live with just 10 slots for 3-star heroes and only put two in each color. This is about all the 3-star you should need to complete every challenge event. Again if you are comfortable with simply collecting the completion rewards and are not trying to compete for ranking.
If you are aiming for top 5% or better on each 3-star tournament then you’d need about 30 slots or 6 heroes in each color. This is assuming you will continue to do some number of pulls in Atlantis, challenge event / costume summonings, etc. Every classic 3-star hero will eventually come your way either through the free summons portal or through a TC20 queue. There are a few classic heroes that are worth keeping if your bench space is limited.
I raid in 3-2 formation and do not have emblems on any 3-star heroes. I’ve placed in top 5% or better in all 3-star tournaments.
Purple: Keep Balthazar, Tyrum and one Bat. You will also need Gil-Ra and Chochin from Atlantis at some point. These latter two are good tanks for purple in any tournament effect. They are also quite useful in on offense in the Rush Attack tournaments. Tyrum is a dispeller, and if you get his costume his cleanse is also very useful. Balthazar is a straight up sniper that will always have a place on an attack team. Bat will be useful on attack teams in all formats. If you eventually do pull Tyrum’s costume, it may be worth getting a 2nd Tyrum because he may very well be on your defense team. If so, his costume will be locked in whatever form is chosen for your tournament defense. Therefore if you want to switch costumes for an attack team, you’d need a 2nd Tyrum.
Blue: Keep one of each Valen, Gato, Ulmer and Gunnar. You might also want a Karil for Rush Attack as his vanilla “hit target + minor damage to nearby” SS damage is a bit more useful when in a trio with Ulmer. Otherwise get a 2nd Gato, a trio of 2 Gatos + Valen is a solid trio in Bloody and Buff tournaments because you can place the Gatos at flank positions on an attack team and use his status ailment immunity cover the whole team. Gunnar is your only really good choice for a blue tank. Level his costume for the stat bump but never use it.
Green: Keep Mnessus, Belith and Hisan. Get a Carver and a Brienne, preferably with her costume. Costumed Brienne is probably a better tank than a Shrubbear because costumed Brienne’s debuff is nasty and scales with each hit. I might even recommend doubling up on Mnessus to get a trio of 2 Mnessus + Hisan for sniping. The sad thing about 3-star raid tournaments is that eventually you will go up against fully emblemed 3-stars on defense and you will need 3 sniper shots to take one of them down. Carver is quite useful in Rush Attack because mana steal / sabotage is the one real advantage in that tournament format. Carver is also a decent tank if you don’t have Brienne’s costume. Shrubbear is a good tank, but sucks at offense. I’m hesitant to even try him in a Ruah Attack offense team as that taunt ability has never been all that useful for me.
Red: Keep Hawkmoon, Bauchan, Jahangir and Rudolph. Add another Bauchan if you get the chance. Well you could also add another Rudolph but that’s like 11 months away. Otherwise get a Namahage or 2. Bauchan is your best tank in all formats. Remember that you will need a trio of snipers eventually. In Rush attack, you might get away with costumed Hawkmoon, Bauchan and Jahangir as your trio and still manage to get a kill or two with one charge of your heroes.
Yellow: Keep Bane and Gan Ju. You will want to add a Pixie, Melia and Kailani. Kailani is your best yellow tank. Pixie is a good SS saboteur and is worth using in all tournament formats. Bane, Melia and Gan Ju / Pixie makes a good trio.