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If you're open to YuGiOh, I recently discovered but have not yet played this
I was able to see it had an extensive deck editor and single-player "campaign" or mode featuring characters from the show. Also, it has online.
There's no word on whether there will be a mode with the normal Yu-Gi-Oh! rules on Duel Links.
There's an older official app that uses them, Yu-Gi-Oh! Duel Generation. It hasn't been updated in a year, it doesn't have Link Summoning, but it might be an option.
An unofficial program that you could use instead is YGOPRO, it has the newest cards and mechanics.
Is it any better than https://play.google.com/store/apps/details?id=com.konami.ygodgtest&hl=en ?
Yu-Gi-Oh! Duel Generation https://play.google.com/store/apps/details?id=com.konami.ygodgtest&hl=en
TL;DR (but not really for pendulums)
Synchros - "Better Fusion" Usually 1 Tuner + 1 or more Non-Tuners whose level = the Synchro Monster's lvl. White cards.
Xyz - "2 = 1" Usually 2 of the same level monsters stacked on top of one another. Uses these materials to activate effects. Black cards.
Pendulum - "Wait...what?" There isn't really a quick primer. They have scales, you activate them in the pendulum zone and their pendulum effects count as spell effects. Set in the Pendulum scales, they're treated as spell cards as well. When they're in the Monster Zones, they're treated as Monsters, and their Monster Effects can be activated and treated as such. Usually "Monster Colored" half, and Green ("Spell Colored") half.
Pendulum monsters go to the extra deck if they would be sent from the field to grave. So, if they're tributed, synchro'd or fused, extra deck face up. Once there, as long as the level of the monsters is between the scales, you can, once per turn, perform a Pendulum Summon, bringing out all monsters between the scales, from your hand and/or extra deck.
Ex. Scale 1 Monster, Scale 8 monster in your scales. Have a lvl 2, 4, 7 pendulum monsters face up in extra deck, and a lvl 5 pendulum monster in hand. Declare pendulum summon. All 4 monsters can be summoned simultaneously as long as you have open monster zones.
There's a great tutorial on Konami's Official Yu-Gi-Oh! TCG Website
Sorry, I know that was a bit much for a TL;DR. But pendulums as the newest mechanic are still a mystery to a lot of people. Reading back, I kinda wish I'd done what /u/Walnnut did.
I actually started with a Synchro/Sawrmy deck when I came back from around the same period. I picked up Six Samurai and it felt like the ultimate version of how the games were back then. Summon a lot, and bring out a relatively large monster or two with a fun effect. But, I also started with the Phone Game, not Duel Links, the other one. Duel Generation.
Helped me learn a lot of the new concepts quickly.
EDIT: Formatting, clarification.