Nichrome 80 is my only choice too. For a regulated mod, 28g looks to be a popular choice for the cores, with either 36g or 38g for the wrap wire. On a regulated mod I suggest trying tri-core aliens 28/36, 7 wraps 3mm ID, dual coil at .2 ohms. I like to think of this as a basic reference, or sweet spot in terms of best flavor performance versus not putting in fairly huge amounts of extra effort to try and get an even better vape. But I only use mech setups, and, I also like to use 27g and 29g a lot. And .3×.1 ribbon of course. The 27g is what I find to be indispensable for making tri-core aliens on a single battery mech, dual coil at .11 ohms, 5 wraps 2.5mm ID. These can also be bought from m.terk, they're on his list of different specs that you can choose between. Essentially, this is the "mech version" of my aforementioned reference point.
Still talking about aliens (sorry about that, but there's a reason why aliens are very much relevant for every coil builder IMO...), switching from tri-core 27g to quad-core 28g doesn't provide a better vape IME, and the former option is easier to make. Whereas tri-core 26g gives too much rampup for my liking. But dual coil at .08 ohms, quad-core 26g at 4 wraps 3mm ID (pic below) does work, if you, like me, prefer a warmer vape with some juices and you know what it all takes to fine tune all the various key parameters to turn that into a vape that's just warm, i.e. not a scaldingly hot one that burns the inside of your lips.
Okay, enough about aliens for now. The coil in your third pic is called the stapled helix build (by a woman named Wire Theory on instagram)... it's an excellent choice of build that I love to use on a dual battery PWM (true PWM) mod. So here's an old pic of a stapled helix build I made:
In my above example I used 32g for the frames, 40g for the wrap wire as that perfectly matches the depth of the groove. It looks rather exotic no doubt, but the flavor performance I find to be nonetheless exemplary TBH. It is a .22 ohms single coil.
As for the 29g, it matches the .3 width of .3×.1 ribbon more closely than 28g does. So I tend to choose 29g to make my fraliens, but I also like to use it for tri-core aliens 29/36, 7 wraps 3mm ID, dual coil at .25 ohms on a stacked/series mech (pic below).