We went to the trouble of watching them in episode air date order, since we didn't want to risk spoilers. That turned out not to be necessary. After the first season, the stories are pretty much separated, with cameo appearances once in a while back and forth, but nothing plot changing, for the most part.
My son watched the first season of Angel when it split off, but ended up abandoning Angel as his time off from school came to an end and just finished the Buffy side. It didn't seem to hurt his appreciation of the series. My younger daughter lives closer and could have kept borrowing the DVDs as needed, but got caught up in the Buffy story and abandoned Angel after one or two seasons. She finished Buffy and is now watching Angel.
Neither of them seemed to be bothered much by the crossovers, except to comment in surprise at how the actor that played Angel had aged after not seeing him for a couple of seasons! I have the same reaction when I go back and see season 1 of Buffy again. "Ohhhhhhhhh! Look how young they all are!"
As far as the Ideal way? Air date order is good, but annoying to get up and switch out the DVD after EACH episode if you are marathoning. My son, when he was still trying to get both series done in a couple of weeks, had one series in the DVD player and the other in the Blue Ray player and just did it all from the couch with remotes.
But that isn't really necessary. Angel isn't quite as addictive as Buffy, so it's really easy to drop Angel and keep going with Buffy. It all depends on how good your frustration tolerance is. They have season long plots all planned out (for both series) , so when they start tossing in lots of cliff hangers, it's hard to switch back and forth when you desperately want to know What Happens Next!
Either way works. Air date or series by series. Or even season by season, if you want to do that.
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