If you want to get a taste of standard, it's sort of the default format on Arena. If you download the client you get a couple of starter decks with it to begin and you can run a few games.
Basilisk
You can also play 1v1 commander with unmodified commander decks, but you need to go into it knowing that some things will be pretty broken while some others just won't work at all. I do this pretty regularly with my fiancee when we just want to jam a few games or if I want to test a deck.
The problem I have with this is that the whole concept of the ring is that it's fundamentally a corruptive force. Without the ring having some kind of outcome where you fall to its corruption, it's not The One Ring, it's just another gimmicky mechanic.
The One Ring should give you bonuses. That's fine - its power is what tempts. But if the ring in the books worked like it does in the game, Frodo should have just power walked into Mordor, slam dunked the ring into Mount Doom, and moonwalked back to the shire, flipping Sauron the bird the whole way home.
The complete lack of any negative aspect to the ring tempting you is just too much of a flavour fail. Maro says that players would not have wanted to use the temptation mechanic if it came with a downside, then they really should have scrapped it and tried something else. Even including some punisher cards that thematically could have introduced a lose condition from being excessively tempted would have been something. But honestly, given how baked in the concept of "undercosted spells or abilities with a downside" are to Magic, I refuse to believe that a free effect of the ring tempting you and giving you a benefit but also a malus would have been unused. There's whole deck archetypes built around that..
I had a few of the cards, enough to make a really bad deck, but never had anyone to play with. Later in university I made a friend who'd played but had given up his cards, and we couldn't really get cards at that point, so we mostly stuck to the Lord of the Rings TCG and Magic.
Other categories I can think of would be "Looting" and "Rummaging", which are cards with the effects "draw a card, then discard a card" or "discard a card, then draw a card" respectively, and "flicker/blink" which exiles a card and then brings it back either immediately or at the end of turn. Also possibly "eggs", cheap artifacts, often 1 mana, that you crack for an effect.
Man, I spent so much time playing Birth of the Federation, and that was kind of a buggy disaster of a game. I really hope this turns out good