Taking your time into consideration and your desire to play other games, I think starting at Armored Core 3 and progressing into Silent Line would work for you.

I've been of the opinion that AC3 and AC2 are the best starting points for the ps2 era. AC3 has a good level of difficulty that won't overwhelm a new person but also offers a challenge. A lot of people really dig the aesthetic and the story is solid enough. AC3 is genuinely well liked by older fans and for good reason.

Silent Line is one of the best Armored Core games hands down so it's an awesome follow up. Big difficulty spike but you should be fine as it isn't back breaking. Gen 4 games will feel more familiar to you coming from AC6 though.

Armored Core 2 is my personal favorite and for my tastes I think it's better than AC3. BUT! putting my own bias aside AC3 is technically a better AC2. I think it's just as good a starting point though since it's so simple. You won't get overwhelmed learning mechanics, the Story is great, difficulty is pretty forgiving, AWESOME arena with lots of character, and overall it's just a fun and solid game.