Someone asked a quite similar question yesterday, but more specifically about WD in the WD forum. Read my reply there, it will be similar, but might have some more nuances.
Now more specifically about group composition:
Ask yourself how long you want to play together, and how determined your friends are. In particular, are you only going to play for like 2-3 hours a night for one week, or for the first 30-50 hours of the season? Usually a season looks like this:
- Pre-season preparation. The more you invest here, the smoother and faster your start will be.
- Start - 2-4 hours: depending on class composition, leveling experience, and how little you mess around, you'll be 70 between 7pm and 9pm.
- Getting the free set: Doing the first four chapters takes around 2 hours. I call that the "pre-set" time.
- Gearing: You have the 6 piece set and breeze through T6-T8, do some GRs to gain quick gem levels, run 1-2 bounties, and do Vaults.
- Early pushing: Sometimes we have fun to push a bit early, i.e., try to get a rank #1 on the first night, or get a high conquest spot.
- Endgame, welp. Congratz if you're still around for that. Usually at around paragon 600-800 there's no goals besides paragon/GR pushing.
For the first two steps, WDs are the absolute king. 1-2 WDs will absolutely boost your leveling by A LOT. However, as of step 3+4, WDs fall behind, simply because their combined mobility+kill speed is not as good as other classes. The other classes are all "meh" for leveling, so it doesn't matter here. For step 3-4, DHs are clear #1 in my opinion, closely followed by monk (though it depends on RNG, or how fast you get In-Geom). That's not to say other classes can't farm easily here; but they're just a bit behind or require much more specific/better gear. For step 5 then, it depends on which conquest/what kind of pushing. Finally, #6 is probably where wizards start to shine for paragon farming, and obviously meta groups for pushing. Important note: DO NOT OPTIMIZE YOUR GROUP FOR STEP 6. Class switching takes 10 minutes in D3, and gearing up a twink takes a day at most if you have a group who helps out.
I'd suggest to go for 1 WD, 1 DH, 1 monk, and the last one being monk/barb/wiz. If you have two WDs to begin with, I'd recommend one WD to at least keep it optional to slowly switch to wizard on day 2; it'll speed up your GR60+ gem upgrade rifts significantly, trust me. For solo, the answer is: Crusader. Invoker is an insane starter set, and lets you easily transition to LoN bombardment, which works up to GR100. Downside: Crusader sucks in groups. And not just "it's mediocre"; it absolutely sucks and does not synergize at all with group play. Crusader in its current state is kind of like holding a sign saying "screw you I want to play alone" (which sucks; I love Crusader and would like to play it in groups).
To add to your tips:
Don't go overboard with the bosses for low-level rare items, don't do it all the way from 1-10. We usually just do bosses if someone feels completely gimped in terms of gear. Which happens after 5-8 levels of doing the kill streaks leveling method. If your group has 2-3 non-WDs, I'm not sure if kill streaks is a good idea; you might be better off doing rifts. (Also because by doing kill streaks you get no mats+gear+gold, so you gain up to an hour over a rifting group but spend more time running T1 rifts at 70 initially.)
After a lot of testing, I personally think that Cain's set is not worth it. You gain a very small bonus of XP, but you spend a lot of materials and gold early on, including the time wasted to get the recipe. And the worst thing is: at around level 35, so 15 minutes later, the level 23 items of the Cain's set are so bad that they gimp your DPS by more than what the bonus XP offers. If you have fun spicing up your leveling go for it, but don't go out of your way. If you get it. make damn sure that at the very latest on level 42 you throw the set away and replace it with rares. Otherwise you run around with DPS-gimping low level crap.
A few seasons ago I did a looooooooot of testing and planning for the level-up stuff. In the end, we shaped off a few minutes, but in no relation to the time invested. A friend of mine did probably 20-30 test runs on PTR for 1-70 and got to 70 first in our region. But 5 hours later their lead vaporized because it's all about drop RNG. In S4 we had a sub-par double barb group wth no goals, but found two ancient HotA hammers and got to #1 early on. Last season one group member bailed on us a few hours before season start, and then we didn't find any decent loot in the first ~15 hours, so our insane planning was all for nothing. Lesson learned: have fun and pray to the RNG gods. If you have nothing to do practice the 1-70 leveling, it will help for the first 2-3 hours into the season, but beyond that there's nothing you can do besides preparing builds.