... currently run an NP435, 4.11's, and 35's.
My Bronco is a weekend driver and doesn't go off road. I want to be very quick off the line and I rarely go over 55 mph.
Then I say 4.56 or 4.88's for you. Then just start in First instead of LOW (or if you prefer, 2nd instead of 1st). I run 4.56's with 30" tall tires, so it sure would not be out of line for your 35's!
And start with the rear only. This way you save a lot of money if you don't like the first choice and decide to go with a lower or taller gear.
You may even decide not to do anything with the front gears and just leave the front driveshaft off, if you don't plan to use 4wd.
Transfer case: Do I need to replace my current Transfer Case?
Your stock case would be a Dana 20. Fairly strong for it's size and weight, but not bomb-proof by any stretch. The heavy duty output is a good upgrade, but the best thing you can do in addition to that is to make sure it's in good shape inside and has the proper lubricant in it to keep things happy.
The good news is that if you go with the lower gearing, such as the 4.88 in the diff, that takes quite a bit of the loading off of things upstream. That includes the transfer case, transmission and driveshafts. The items left downstream that you have to worry about at that point are the axle shafts and, if you really hammer on it during your daily routine, the axle housing itself.
Keeping the taller 4.11's with 35's keeps more stress on all the upstream parts, right up to the engine.
And lower is easier to get the hole shot...
Not always something that Bronco owners discuss, but better acceleration seems to come up more and more these days.
I have read a lot of great things about the NP205. And it looks like the Atlas may be the best option, but it's expensive.
Yes, the 205 is probably stronger than the D20 even with the HD output. It's just beefier. And since off-roading is not sounding like your thing, the taller 2:1 gearing of the 205 vs the 2.46 or lower of the D20 is not a detractor.
Agree that, while the Atlas is 'da bomb in transfer cases, it's not needed for what you're talking about and one of it's main claims to fame (the optional lower gearing) is not really a big benefit to you.
Gears: Should I stay with 4.11's or go to 4.56's? Or another option?
You already know my feelings on that, but I'll say again that I think the 4.88's would be more fitting for what you are describing as your preferences in performance and driving.
Drive shaft: Do I need to upgrade from the stock drive shaft?
I would have to say "maybe" in this case. Depending on how patient you are, you might just drive on the stock t-case and driveshafts to see if you break them or not. If you go with the lower gearing you are taking some of the load off of the shaft, but whether or not that's enough is going to be up to your right foot ultimately.
You would do well to consider running 1330 or 1350 series u-joints. Which would entail new yokes for the transfer case and the rear differential. And the new shaft with the bigger joints.
As much as I'm a fan of doing some things locally, we would have a better price on a high quality shaft of your choosing. We use Tom Woods for most of our shafts and can have custom ones made to your specs pretty easily and quickly. And likely much less expensively than a local shop could do it.
But even the heavy duty "Extreme" shafts we sell would be a light upgrade over your stock ones. Same size u-joints, but smaller diameter, thicker tubing helps with torsional stresses without the bulk of a very large diameter tube.
Should I buy from WH's or have one built locally? I do have a shop that specializes in drive shafts (heavy duty trucks).
Love to sell you stuff of course(!) but it would not hurt for you to at least stop in and see what they have to offer and for how much. It's usually good to have at least a basic relationship with the local guys if you like what they offer.
If not quite sure, we're still here for you.
Rear axle: Do I need to upgrade from my stock rear axle?
As mentioned already, yes and no. The Ford 9" housing and third-member and gears are very robust (usually) but if you're planning to have "a lot of fun" with this setup, a heavier duty housing is not a bad idea. And really not that expensive.
But upgraded shafts are a must. The stock 28 spline shafts were great for the size tires and expected uses that Broncos had when they were being built. But if you add more power and more tire, you need more shaft.
And if you add a limited-slip diff, or worse still a locker of some kind, a shaft upgrade becomes even more critical.
Your choice for the two most common upgrades. 31 splines and better material are quite a bit stronger, but if you're not sure it's enough, go big with the 35 splines. The remaining upgrade from that is a better-still material. For at least some of our 35 spline setups we use Dutchman which have an optional special alloy available over and above the normal special alloy. Should be VERY strong for minimal higher price.
But for 35's you also have to upgrade to the better/bigger center sections like the Nodular Iron versions mentioned. They use the larger carrier bearing size that allows the larger diameter 35 spline axles to fit, where they would not in a stock type setup.
Housings are easy as point and click. Here are a couple of excellent choices that we offer at least. The HD Super 9 and the Megalodon are the first two items on this page:
http://www.wildhorses4x4.com/category/Bronco_Rear_Housing and run the range of quick-n-easy offerings. The nice thing about buying something like these from a Bronco vendor is that the extra large perches are welded on at the correct angle for most lifted Broncos already (at least I know ours are), so you don't need additional shims to correct improper pinion angle. Not a big deal, but a nice little extra.
At $489, the Super 9 is a pretty good bang-for-the-buck candidate.
The Megalodon is overkill for most, but not for all. And the bragging rights at stoplights and the parking lot conversations started when someone eyes one of those things under your rig are priceless!
I usually recommend clear-coating them instead of painting. This keeps the look of the fully fabricated housing, without the eventual rust issue.
If you go to junkyards anyway, you can keep your eyes open for a vehicle that had a custom rear end already (not common, but they're out there) for the best price. But you likely won't find one that's the appropriate size or feature level in anything but another Early Bronco. Good luck on that in most areas!
One thing we didn't touch on is steering linkage. With the larger tires I would upgrade to a stronger steering link if you have not already. Something like on this page:
http://www.wildhorses4x4.com/category/Custom_tie_rods such as the #2351 for '66 to '75 front axles will give you not only the added adjustability to compensate better for lifts, but a much stronger tie-rod to eliminate or at least reduce the deflection that larger tires can cause. More stable wheelies and drifting don't you know...%)

;D
Usually multiple choices out there. But this'll get you started. Hopefully we have at least some of the parts and info you need to get what you want from a performance and reliability standpoint.
Paul