Depends on how you play.
If you've got a group of people to play with R6: Siege is outstanding. It works well as both a sweaty, go-big or go home competitive experience, but it also works well as a game that you can fuck around in and make some weird, outlandish plays in. However, if you're solo-queueing then the toxic community might be a bit of a turnoff. That said, Siege is also a very slowly paced game, and if you try to play fast and loose you'll likely get frustrated quickly.
Overwatch is in a similar boat, great with friends, terrible toxic community that can sap your enjoyment if you're solo-queueing. Overwatch is also much faster than Siege, so if you're looking for something less methodical and more manic, it might be worth trying.
A major problem with both games however is that you've got a lot of learning you need to do in regards to character picks and counter picks. There are 48 operators in Siege and 30 heroes in Overwatch. Each of them is tailored to do something specific and what's more, each of them has unique interactions with other player's characters. So you not only need to memorize what your character does and how it can be most effectively utilized, you need to learn how your character interacts with other characters. Then you need to learn which characters counter other characters, ect. ect. It can be a bit of a logistical nightmare.
If you don't mind an older shooter, Battlefield 4 still has a very active playerbase and it works incredibly well as a game you can just pick up and play; you can get all the base game and all the map-packs for next to nothing and I'd consider BF4 one of the greatest multiplayers of all time.
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