The old style was fine, just more of a focus on stealth over combat, the real problem was running the formula into the ground with like 8 annual releases.
The modern story was a lot more prominent and coherent in the first few games, until it was more or less wrapped up in 3/4.
That said, I haven't played them myself in a while, and I imagine 1 is rough. You could probably youtube the important stuff and skip to the Ezio games.
The original game looks great with the One X enhancements, but it's very repetitive and clunky by modern standards. I remember even in ~2012 people recommending to read the story online and dive into AC2. I fired it up to see how it looked with the facelift and it was okay to dabble in for a few hours, but I definitely didn't have the patience to do more than that.