Generally the marker of M+ applications is RIO score, which you can’t see in-game per say. There is an addon that allows you to see it.
It’s essentially a score calculated from which dungeons you’ve successfully run in-time and what the highest key level was for that dungeon. The more dungeons you run in time, at higher keys, the higher your score. Although you only get score for each specific dungeon at the highest level you’ve played it.
Example:
If I time a Freehold +2 I get 20 RIO
If I time a +2 Underrot I get 20 RIO, so now I have 40 RIO
If I time a +4 Freehold, my Freehold score gets boosted from 20 to 40, so now my total RIO is 60.
etc.
So when looking for keys a general level people look for is that you’re within a short distance of having shown you’ve cleared all dungeons at around the key level just below the one you’re applying to. There are 12 dungeons so that’s 120 RIO points per key level to satisfy a “tier”.
So for example when applying to a Freehold 10, people will be looking for a RIo score that sgguests you’ve timed +8/+9 keys regularly which would be a RIo score of around 920-1080.
For +2s people probably want to know you’ve “done” some mythic before, so having a score above 0 is advisable, the higher it is, the more likely your chances of getting in.
Ilevel is a secondary concern, but largely after RIO. So for example you may have 1200 RIO because you’ve run lots of keys with your mates, this suggests you have timed +10s across the board. However if your ilevel is 430, you probably still won’t get invites because your gear is technically too weak, and with a score that high it suggests you’ve been “boosted” through those keys, which means someone making a group will probably avoid inviting you for fear of you not pulling your weight. The same score on a 450ilevel would probably get invited no questions asked assuming someone with either a higher RIO and/or ilevel isn’t applying to the same key at the same time.
So to get regular invites as a DPS involves a lot of running dungeons to evidence your RIo score to “prove” you’ve run them successfully before, and making sure you get a variety of dungeons whilst doing so. If I only ran for example Tol Dagor, KR and Temple, even at say +15, that still only adds up to 450 score on their own, which means most people will outright ignore my application to even a +13 for those keys. Some people may check my profile to see that the score is from those keys specifically, so i’m actually a good invite, but most just look at the score number alone, outside of context, so it’s very important to ensure you pad it with as many dungeons as you can at the highest levels you can do.
This is very tricky in the beginning, which is where the communities come in. They allow you to get in the door, once your score starts to build you can then start to PUG the dungeon keys you’re missing to build the score on your own. Once your score is pretty solid, invites are much more likely.
My hunter has a very unbalanced RIO atm (i’ve done +13s/14s/15s but only for 6 of the dungeons) and he has 463 ilvel but I will still be declined invites for even 8/9 keys for those dungeons i haven’t done because my RIO is too low, even if my ilevel suggests I am overgeared for it, because my profile provides no proof i have experience of those dungeons at a similar level. So I either have to run those missing dungeons at a lower level to build them up, or I have to hope someone does invite me for them at some point because then i’ll fill that gap.
PUG life as a DPS isn’t easy on your own and requires significant investment, which is why i’d suggest communities above all else. Zen Horde and SoD do not use RIO when making their own groups for example. When running their highest keys however they may insist you’ve done similarish before, but that’s largely for the people who are dedicated “key pushers”- generally speaking there is always room for people to get their 15 weeklies done during the week i’ve found. It’s keys higher than that where they begin to expect a little bit more in terms of “do you know what you’re doing”.