The first is, ISTR, dead-on accurate - though the second will do too and involved less disc switching!
I'm watching it all via Netflix, so disk switching isn't as much of a problem. The first it shall be, thanks very much!
I put together some similar lists a while ago - there are some episodes which have to come in a specific order, and others that don't matter. For instance, Buffy #4.1 comes before Angel #1.1, but it doesn't matter whether you watch Buffy #4.2 before or after Angel #1.1. So, you could do two episodes of Buffy, then switch to Angel, or alternate back and forth between them, depending on your preference. That means that it will be hard to come up with a definitive list.

Having said that, I've had a quick glance at the Google Answers list and I disagree with that - according to my notes, Buffy #4.8 has to come between Angel #1.7 and Angel #1.8. (They have #1.8 and #4.8 the other way around.) Similarly, Buffy #4.21 has to come before Angel #1.21, and the Google page has them the other way around.

So, here's my advice on viewing order. Some episodes are closely linked, so ideally you would watch them back to back, depending on how much time you have; I've indicated those with a *.

Buffy #4.1-#4.2 *
Angel #1.1-#1.2
Buffy #4.3
Angel #1.3-#1.4
Buffy #4.4-#4.7
Angel #1.5-#1.6 *
Angel #1.7, Buffy #4.8, Angel #1.8 *
Buffy #4.9-#4.11 *
Buffy #4.12
Buffy #4.13-#4.14 *
Angel #1.9-#1.17
Buffy #4.15-#4.16, Angel #1.18-#1.19 *
Buffy #4.17-#4.19
Buffy #4.20-#4.22 *
Angel #1.20-#1.22 *

Buffy #5.1-#5.7
Angel #2.1-#2.11
Buffy #5.8-#5.17
Angel #2.12-#2.22
Buffy #5.18-#5.22

Buffy #6.1-#6.3
Angel #3.1-#3.4
Buffy #6.4
Angel #3.5
Buffy #6.5
Angel #3.6-#3.20
Buffy #6.6-#6.22

Buffy #7.1-#7.16
Angel #4.1-#4.14
Buffy #7.17
Angel #4.15-#4.22
Buffy #7.18-#7.22

I've been meaning to rewatch my DVDs, so I may tweak this list as I do, but I think it's as good as any.
You're welcome. I suppose the best solution would be to use project management software: that way you could set up a Gantt chart for all the dependencies between episodes, while still having some flexibility to choose which series to watch next. However, that might be overkill :)
My suggestion: stick with Buffy & don't bother with Angel. The only goods thing in it is Daniel Dae Kim and he's only in 12 episodes...
Hmm, the completist in me probably won't allow it, but duly noted. :)