For the elite queue or future ranked system you should reward points for:
Kills: 1 kill = 1 point
Rings alive: 4th ring and after = 1 point each ring
(there are a total of 6 rings if we don't include the one fully covered the map, that way camping won't be that easy and rewarding, on top of that living all the rings gives you a total of 3 points making it worth living until the last ring just to pay your fee for the next match)
Dmg dealt: 400 damage = 1 point
(that way even if you happen not getting the kills you still get rewarded)
Winners/ Champion Squad: 2 points + 1 point for each player alive (3-5 points depending how many teammates alive)
(with this method you encourage people helping their teammates out to guarantee those extra points, also skilled players will always be rewarded even on bad games if they haven't secured their kills)
Points will determine with what players you will queue against.
Let's say we got 5 ranks:
Bronze : 0- 50 / each time you get into a match you pay 1 point
Silver : 51 - 100 / each time you get into a match you pay 2 points
Gold : 101- 150/ each time you get into a match you pay 2 points
Platinum : 151-200/ each time you get into a match you pay 3 points
Champions : 200 above/ each time you get into a match you pay 3 points
Apex Title: Will be rewarded for a certain amount of top score players in the champions rank.
If people ask me why the same amount of points should be paid in 2 different ranks. It's because the higher you rank up, the harder it will be earning those points, so making the fee high from so soon would make an unhealthy enviroment for the competitive system.
So to earn that apex title you need to earn points, or else you will be kicked by someone who actually tries.
Last and least i would add in the ranked games a passive that makes people to start losing hp like they are in the zone if they don't have a certain amount of damage dealt for the required zones. That way players that land in areas with other players and make it out alive, wont have to worry about some of the rings depending the damage they dealt, while other that prefered to loot safely will eventually need to reveal themselves from hiding and show their position.
Lets say for example:
1st ring= 50 damage needed
2nd ring= 150 damage needed
3rd ring= 300 dmg needed
4rth ring= 450 dmg needed
There is no need for the passive to exist later on since the zone is already small enough while the rings closing much quicker than before eventually players will have to fight. Think this as a check up, players that are willing to fight and are skilled won't have a problem with this passive and eventually they earning those points given after surviving from the 4th ring and beyone, while those who didn't will end up dying or using a lot of resources to heal up, ending being prey in the further rings.
On top of that this passive brings more depth and strategy into the game of where you might wanna drop or during the drop you might want to follow another team that tries to fall in a isolated area so you can secure the damage needed or even just trade some hits so you secure yourself the damage and leave.
NOTE: Don't give attention so much into the value of points rewarded rather how the system would work out, the numbers could be adjusted later on since there was no crazy math behind this idea.