Tales of Zestiria

The last Tales of game that I played was Tales of Innocence and that still had the TP system, so this new battle system confuses the pomegranate out of me.

I was able to try Tales of Graces f on a friend's PS3 a long time ago and it feels similar to that. Did they do away with the whole Basic Attack-->Base Arte-->Arcane Arte thing?

haven't played zestiria but yea it was that way in graces, you had to figure out what could combo into what mainly.

In Graces, you basically had Artes Style artes go A1->A2->A3->A4 as a hard restriction for combos. You could mix any Burst Artes (the other button) in anywhere though, and those could be spammed as long as you had CC. i.e. A1->B->A2->A3->B->A4
In Xillia, you could use any arte in any combination (unless there was an aerial restriction) as long as you had TP/AC.
In Zestiria, it's similar to Graces's with Martial Artes, M1->M2->M3->M4, except instead of inserting Hidden Artes into the combo, you replace an arte in the combo. M1->B->B->M4

One of the reasons for people who didn't like Graces's system was because they were forced to execute a strict combination, despite there being 3 to 4 different optons for A2/A3/A4, and a very wide range of Burst Artes.
I personally dislike the Basic Attack -> Arte -> Arcane Arte because basic attack is pretty worthless and uninteresting, and only an artificial way to generate TP. There were typically a large number of Artes to choose from, but it felt like it was just to progress to the more powerful Arcane Artes a lot of times. Like, this base arte does more hits to build a combo, or this other base arte is mathematically stronger, not because it was particularly useful for any effect, and they all just provide the same opening for an arcane arte.

With the more recent titles, intermediary artes are used to mix in damage/weapon/element types, and many artes have either different combo set-ups or certain effects. Particularly in Zestiria, many artes have buffs or debuffs.
That's not to say that the older games didn't have combo set ups, but there's a lot of freedom, especially in Xillia 2 where you literally have more artes than you can map (IIRC 18~20 vs 16 shortcuts), and the vast majority could combo into each other. The exceptions were basically artes that put you in the air, meaning you had to use another arte that could be used in the air, or something that had knockdown, forcing artes that could force enemies to stand (which itself was well set a combo). In Vesperia, Yuri had 10 Base Artes, 14 Arcane Artes, and 10 Altered Artes. IIRC, you could do 2 different Base Artes, 2 different Arcane, and 2 different Altered in one combo before being forced to stop. Some just left you pretty open with no options. Some combinations just couldn't work. I really don't feel that in any of the newer titles, unless the enemy got super armor in the middle or you used something they resist.

Sister picked up her CE, but we won't be playing it until she gets back this weekend and after we finish Graces F since we're right at the end in the final area. I read they didn't really do much to the PS4 version other than increase the draw distance and other stoof. Camera is still balls.

Avoid walls. Just avoid trying to fight near a wall or doorway. It's fairly simple to get used to unless you get ambushed. If it does happen, you can fix it by moving away from the wall most of the time though, in my experience. Might be harder to coordinate when the camera focuses on P2 as well though.