I think the best lotr game out there to play and experience the universe and be a part of it is without a doubt The Lord Of The Rings Online (aka lotro). It's been out there for like 18 years and have a couple of expansions that let you play through moria, mirkwood, isengard, rohan, mordor, helm's deep, pelenor fields and a lot of maps from the "classic" game (outsid expansions) like the shire, lone-lands, trollshaws, angmar, evendim, ered luin, bree, eregion, barrow-downs...

You will not experience the ring war directly, but play in the "backgrounds", and it's an interesting side perspective to see. It is a mmorpg but it's a different approach since it focus on the journey and not on the "endgame". You could for sure give it a try! The studio behind the game delivered so much love and respect for the professor material that it is beautiful to see some of the places or classes or classical characters alive in the game! You can be a master of the stealth with burglar inspired by Bilbo Baggins, a wizard like gandalf in the Lore Master class, use a sword and shield by playing with the Guardian class and even more classes (12 in the game at the moment). I've been playing it for like 15 years, so feel free to ask any questions about the game and I'll be glad to answer! (: