Raid Minimums
Virtues
Minimum T1: 5 active virtues must be 77+
Minimum Challenge T2+: 5 active virtues must be capped (currently 82)
Recommended: Cap as many virtues as possible for passive bonuses. It's better to cap a single virtue at a time because the bonuses really accelerate from 60+
How we'll help: Occasional deed runs, e.g. Moria instances Saturday afternoons

Trait Points
Minimum T1: 95 trait points
Minimum Challenge T2+: Capped (currently 98)
How we'll help: Big Battle runs on request for promotion points, or to progress the epic (e.g. Gondor big battles)
Legendary Items
Minimum T1: Purple (Rare) rarity traceries, 465 enhancement rune level on each
Minimum Challenge T2+: Blue (Incomparable) rarity traceries, with Gold (Legendary) recommended. 480 enhancement rune level on each
How we'll help: weekly LI advancement runs. Also see the LI Guide page.
Stats
Minimum T1: Player is in full 460 purple gear, with class / role appropriate stats (purple gear is available via crafting).
Minimum Challenge T2+: Expectation is that player is in 465+ purple gear from AoD / DoP / HoR / HH T1. Ideally, players have 2-set bonus from T1/T2 HH. Also require class / role appropriate stats.
Raid leads may request screenshots to validate build.
What do we mean by "class / role appropriate stats"? See LOTRO HQ for more information on what the broad consensus is here, though by no means is that site the ultimate end all, be all for what is viable. Ask any of the officers in-game if you have questions!
How we'll help: Not a straightforward path here, but just ask in-game if you need a particular run, a questing buddy, etc.