Should I write it, or should I somehow find a way to connect the stories in novel format? They'd all include at least one recurring character, and for the most part all be based in the same location, but take place at various times over at least a few years.
Interesting concept. I like the idea of taking one character on a significant journey in their life, then introduce another one who takes the main focus, and so the former character becomes a backdrop as you develop the next one. That would be a rich story, in my opinion.
nobody can make that decision for you... either way can work, if well-written, but if you're new to writing, you might want to hone your skills with short stories, before tackling the fiction writer's 'everest'...
It depends entirely on you how you develop the plot...both will work well depending on how you stitch the seams. I guess I would like to see it as a series, since your characters are spaced out over time. Still, you've got to use your best judgement on which technique works best.