As far as clear objectives, I want the vast majority of champions to have around 6-7% global average pick rate, no champions with less than 2% pick rate, and for no champion to have more than 14% pick rate or more than 25% ban rate. I want no champion to have more than 55% winrate or less than 44% winrate on global average. I want no champion to vary by more than 14% average winrate across the skill gap of Bronze IV - Diamond II. Outside of that range, I think outliers are harder to control and less reflective of champions' actual power levels, so the far ends of the skill spectrum should be balanced more loosely to find their own metas but still factored into global average statistics.
For subjective goals, I want team composition to matter a lot and I want every role and class to feel valuable.
I want supports and utility/tank champions to feel more rewarding. I specifically want supports to have more freedom to roam and support their whole team during laning. I want a meta shift where everyone wants the support to visit their lane (to drop them some heals, poke the enemy, etc.), instead of the support feeling like an unwanted XP leech. I want autofill to be unnecessary because support is made into an actually desirable role.
I want ADCs and APCs to have overall equivalent carrying potential and for carry mages and marksmen to be able to flexibly go mid or bot depending on team composition and player preference. I want teams to feel that they need both sources of magic and physical damage in order to successfully take down the enemy frontliners, and I want the frontliners to feel like they can capitalize by itemizing either armor or MR if the enemy team doesn't have a good mix of damage types. I want marksmen to do somewhat less damage lategame and to gain utility to make up for it, such as shredding enemy resistances for their team and granting vision like Ashe's E.
I want assassins as a class to be balanced around other strengths than 100-0s and snowballing. For example, I want champions like Shaco to play more mind games and control the map with box traps, and I don't want him frequently straight up bursting people out of stealth. I want Nocturne to play mind games and strategic vision control with his ult, and not just kamikaze diving squishy champions for virtually guaranteed kills. I would love to see some clever saboteur and trap-specialist assassin items added.
In general, reducing snowballing will help make the game feel better in a lot of cases.
I want the meta to look kind of like this:
#Top: heavy frontliners



>opportunists

#Jng: heavy frontliners



>opportunists

#Mid: squishy backliners




>opportunists


#Sup: squishy backliners


==heavy frontliners


>opportunists

#Bot: squishy backliners





General Team Comp: ~2 frontliners, ~2 backliners, ~1 opportunist, overall average damage composition 55% physical + 40% magic + 5% true damage
Some champions, like a lot of divers (opportunist + frontliner) or champions like
(opportunist + backliner), overlap between team composition roles, so actual team compositions wouldn't completely follow this formula. Also the meta shouldn't be so strictly enforced that it would be represented in every individual game. I just feel these should be roughly the average breakdown over a large number of games.
For example, you could have these two team comps and they would come out to following pretty close to the formula above on average:
VS
Or
VS
etc.