ME:A sounds like it'll be more your style, then. The combat and movement have been vastly improved, the older games always had you feeling "locked" to the ground, and the movement and cover mechanics were always really finnicky, especially considering a lot of the combat takes place in fairly cramped spaces clearly designated for combat (waist high boxes in rows spaced out ten feet apart, gee I wonder what's going to go down in this room).
ME:A falls into this trap somewhat as well, but the new movement mechanics have you zipping around the battlefield and blasting enemies like Vanquish. It's really, really fun and there's a ton of variety in which abilities you decide to put skills into. There aren't any rigid classes, so you're free to experiment with different abilities and develop your own playstyle. Right now I'm playing a standard Vanguard build, which means I can teleport to an enemy which hits them with a biotic punch as I come out of the teleport, which I can then follow up with an AoE slam into the ground, then put up a barrier to deflect bullets and defend myself if I get too much heat. Once my cooldowns are up I can teleport to a different enemy in another part of the combat zone. It all feels really fluid and kinetic, it's just a joy to play honestly, and it's really easy to develop a build that plays well off itself given the flexibility of which abilities prime an enemy and which ones detonate them for an explosion that deals extra AoE damage.
ME1 had an exploration mechanic, but it was rightfully dropped in the sequels because it was pretty dreadful. Planets were basically just one huge texture and some mountainous bumps in the terrain, almost never any plant or animal life. It was like if every planet in the universe was the moon with a different color of neon lighting. 2 and 3 go for a more tightly focused experience, but it was a little disappointing that they followed up ME1's planet exploration with...well, not really anything.
I guess what I'm getting at is, it sounds like ME:A does the things you're looking to enjoy better than the previous titles. And who knows, maybe you'll find the whole package more enjoyable without the baggage of the original trilogy on your mind.
