What is the best speed? On exrx, the lady takes about two seconds for
one full rep (up + down). When I concentrate on pulling with my
arms/shoulders mostly, I take about ten seconds. When I do it faster,
I can't concentrate on my arms so much. What's better?
The stronger you get, the faster you'll be able to go. If you get to the point where you can do one-arm pullups or with 1/2 your bodyweight in plates hanging off you, a regular bodyweight pullup will need to be force-ably slowed down to keep yourself from whipping about.
I wouldn't concentrate on any particular areas though. One of the great things with compound movements like that is that they're fairly natural, so your body will eventually do it with the appropriate amount of muscle activation. Your big muscles (lats, in particular) will handle most of the load and your smaller muscles will take a back seat, which is exactly how it's supposed to work.
Go as fast as you can on the way up, but specifically on the downward (eccentric) side, make sure you don't drop like a stone. You want a controlled release so you don't shock load your arms.
How should I organize my workout? Should I count reps, or go for time,
or a hybrid or what? Either way, I can't guarantee that all reps will
be equal as during the set or from set to set, my arms/back become
weaker and my legs do more.
Unless you have some rather specific reason to do otherwise, I'd recommending shooting for 3 sets of 12. Both with dips and pullups, I've seen good results making sure you can do a lot of reps (10-12). When you want to target strength specifically, you might drop that down to 5 reps.
On an intermediate program I have good luck doing 3x12 on one day (Monday), then 3x6 weighted on another day (Friday).
How can I track progress? I have a strong on-off relationship with
training, so I want something that allows me to track progress to keep
me motivated, also I want to be sure I don't stall.
I've never done self-assisted pullups, but I imagine that pushing your legs out in front a bit will reduce their power. Likewise, letting one leg go a little "limp" and not tensing it will reduce your leg power.
The big thing I'd try to do, and that you should use as a gauge of progress, is how much you're able to take your legs out of the equation. The less reliant on them you are, the stronger you're getting.
Another thing I'd really recommend, and that you could incorporate in what you're doing right now, is negative pullups.