"Official" events are going to be either "limited" or "constructed" - in limited formats you're given some number of booster packs to build a deck on the fly, and in constructed you're bringing a deck that you've pre-built at home using cards from your collection. For that reason I'd probably recommend limited events to start, as if you and your SO are still pretty new you may not want to shell out $$$ for a good constructed deck, only to find it isn't a style of deck you enjoy playing or that the deck has "rotated" out and is no longer legal by the time you're comfortable playing it.
Limited events come in two major varieties, draft and sealed. In draft, you sit around a table of ~8 players. Each player opens a booster pack, picks the card they want most, and passes the rest around in a circle where the next player picks a card and passes the rest along. You do this until each pack is depleted, then usually repeat the process with two more packs. Then you build a deck out of your cards and play against other members of your group. Draft can be a tricky format because you have to be good at evaluating cards very quickly and making quick decisions about whether to take a higher-powered card or a card that fits better with your previous picks. But it's also very rewarding when a draft goes well.
Sealed is a bit similar, as you're given six packs, open them all together, and build a deck out of what you open. No exchanging cards with other players, and you see everything at once so there's less gambling / hedging involved. Definitely a more accessible format than draft, and it's also good for building up your collection. You won't always open powerful top-tier cards, but you'll always find fun commons and uncommons to brew casual decks out of at home.
On the other hand, there's constructed, where you bring decks you've built in advance. Constructed events usually fall under one of three formats - standard, modern, and legacy - each with different restrictions on what cards can or cannot be played. Standard decks tend to be the least powerful and cheapest, using only cards printed over the past 18 months or so (with some exceptions). That means building a standard deck is pretty easy, but cards are always aging out of the format so you'll have to update your deck or build a new one every few months.
Modern and legacy are "non-rotating" formats, which means cards never age out and once you build a deck you're usually safe to play it forever (sometimes cards get banned for being too strong but it doesn't happen super often). Cards printed since ~2004 are legal in modern, while cards printed since Magic's inception are legal in legacy. So, as you can imagine, these decks tend to be higher powered, more skill intensive, and much more expensive. Probably not a good choice for newer players, but a great option if you get your bearings and want to invest in a deck that you can keep perfecting for several years.
Then there are other "casual" formats - your local store might have EDH / Commander nights which are a ton of fun and worth looking into. That's another good place to start in my opinion, those formats tend to get played in big multi-player groups so even if your deck isn't the best you can often win by playing politics and being sneaky with your plays, forcing your opponents to kill each other while you stay back.
Most stores are going to at least have draft and standard weekly, and bigger stores will usually have more formats too. Sealed usually comes around with the release of each new set, so that might be a good time to get involved at your store.