Please box spoilers if you must post them.
I am just about to finish season 3 of Buffy, and I understand that Angel splits off at that point. Should I watch season 4 of Buffy and season 1 of Angel at the same time by interleaving episodes (ideally in the order they were originally shown), or is there really not much crosstalk between the series and I could watch through a season of one and then a season of the other?
There are a couple of nice crossover moments, actually - especially Season 4 of Buffy and 1 of Angel. Once you get to Seasons 6/3, you can skip the interleaving.
There is very littel corssover in the series. I think there is one ep in season 4 of Buffy that continues on an ep of Angel, but I might be wrong. I do know that Buffy is on Angel once or twice, and visa versa with Angel, but there’s not always a set up in the other show to indicate that.
I’m doing this right now, watching Buffy season 4 and Angel season 1 concurrently. I’m trying my best to go back and forth, one by one, duplicating the original viewers’ experience, but sometimes I get on a streak with one show or the other. There are a few crossovers that you can really watch in any order you want, but will be more satisfying if you follow the Buffy episode with the corresponding Angel episode.
The early one has Oz and Spike going to L.A. and interacting with Angel after the events on Buffy’s show lead up to it, and a second crossover has Angel appear in Buffy’s Thanksgiving episode, followed by Buffy following him back to L.A. on his own show (and that’s a classic).
Attempt to come up with a quick crossover guide:
Buffy 4.3, “Harsh light of day” followed by Angel 1.3, “In the dark”
Angel 1.7, “Bachelor party” leads to Buffy 4.8 “Pange” leads to Angel 1.8 "I will remember you
Buffy 4.16 “Who are you” leads to Angel 1.18 “Five by five”, Angel 1.19 “Sanctuary”, back to Buffy 4.20 “The Yoko factor” (You can take some time before making the jumps in this one, so long as you get them in order.)
Buffy 5.22 “the gift” should probably be seen before Angel 2.22 “There’s no place like Plrtz Glrb.” There’s a few interrelations in early angel season 3 and buffy season 6 that I don’t have time to go into right now… they’re not particularly important though.
Buffy 7.17 “Lies my parents told me” has a leadin to Angel 4.15 “Orpheus”… (they messed up this one even by the original air dates,) which leads back to Buffy 7.18 “Dirty girls”
Angel 4.22 “Home” leads into Buffy 7.21 “End of Days” and Buffy 7.22 “Chosen”
Hope that helps you. I might go and try to include the missing patch for a sense of completeness.
Okay, I’ve got it, not as complicated as I thought.
Angel 3.1 “Heartthrob” follows on from Angel 2.22 “There’s No Place Like Plrtz Glrb” and refers to Buffy 5.22 “The Gift”
Buffy 6.4 “Flooded” and Angel 3.4 “Carpe Noctem” end similarly, and Buffy 6.5 “Life Serial” and Angel 3.5 “Fredless” start similarly. Don’t think an exact order matters, but you should probably watch them all around the same time, and the earlier ones from each series before the later ones. K? 
Buffy 5.7 “Fool For Love” is part one; Angel 2.7 “Darla” is part two of an excellent crossover.
You should watch S4 Buffy and S1 Angel at the same time. The best way is to watch Ep1 of Angel, then Ep1 of Buffy (there’s a moment in the Buffy Ep that’s clearer that way); thereafter watch an episode of Buffy and then an episode of angel. After the end of that season it doesn’t really matter. The timelines uncouple from that point, so it’s not really clear when the two shows are happening relative to each other
But I would watch Buffy first since their are so many one way crossover characters.
This order is simple and seems consistent with the dependencies listed above. Now I just have to deal with the annoyances from changing discs a whole bunch. Maybe I’ll just buy another DVD player…
It is sad how many times I have considered buying a DVD changer so I could watch (nearly) complete seasons of TV (mostly Buffy, Angel, Firefly and Sports Night) without, you know, moving.