The new series needs all aspects of the group formula.
Friends, family AND romance. That was the formula of both shows before it.
It wasn't only two groups of platonic friends and a total rejection of biological family in favor of only "found family". That's disingenuous. It's utterly false. That's saying that Joyce, Dawn and Connor weren't important parts of their respective casts because they were only there as family, yet were obviously more important to the main characters than anyone else in their casts. Half of the Scoobies were really just there when they were the boyfriend/girlfriend of a core Scooby and left when they broke up!
And I would bloody start with Buffy Summers herself having some kind of family structure around her and not a dwindling group of fragmented friends who only pop-in occasionally with the glaring fact that Dawn and Xander can't be in the picture anymore.
Given that she herself could easily have a teenage child or children, that's one way you could believably begin to fill out the young cast around the new Slayer in a very organic way that isn't just a repeat of the new Slayer meeting some new friends on her first day transferring to a new school.
The question would be if this hypothetical child of Buffy (whether by Shanshu'd Angel or just some dude, though I wouldn't recommend it--especially if he were made absentee, which would be all of Buffy's abandonment fears come true) would be aware of all the family secrets already or would be learning them right alongside the new Slayer. That's one way to differentiate the shows and the younger cast member dynamics.
And yes, you're going to have to probably have a few characters amongst the younger set who are a bit supernatural themselves. And those characters are going to be obvious picks for major romantic leads.
I would avoid any more vampires with a soul (done twice, it would further damage the uniqueness of its original usage and add an uncomfortable morality conundrum to Slayers having the moral right to slay without remorse), which pretty much limits use of any romantic vampires at all because of the mythology rules not being comparable to other vampire romance dramas.
I would heavily back using a half-demon (especially given how short Doyle's storyline was, which had plenty of material for a character with a demonic side who was raised human) or demon love interest instead. The Buffyverse already had something like this with Anya, though waited far too long to deal with the consequences of having a love interest who showed little remorse for a past that was arguably worse than Angelus and Spike combined.
Another way of working supernatural members into the group would be giving someone a special power or becoming magical over the course of the story, whether they be given visions like Cordy (which killed her, lest we forget) or Willow becoming a witch. Probably a safe bet there will be a magic user in there.
Buffyverse werewolves are unfortunately rather limited in the sorts of stories that get told about them with little actual ability for the characters in human form and end up just becoming MotW filler to pad out seasons. The difference with the vampire love interests is that their species doesn't just turn on for three nights a month and they can't pretend they're mostly human.
I still say there should be a stronger delving into the Watchers' Council mythology and history. I think adding a Watcher character in addition to Buffy's mentor/mother role would be a good idea for building the group dynamic. Buffy is unlikely to work as the main researcher of the group, though characters like human!Angel or Giles could conceivably provide a lot of exposition information. Probably need to bring in a younger Watcher character, perhaps.
The Old Ones would be another interesting route to go. Wolfram & Hart and the Powers that Be are still juicy concepts that could play a part, given they still remain undefeated and unanswered as to what their full plans were. I'd avoid the First Evil unless they massively retool its presentation.
I really do think we need answers about the end of Not Fade Away just as badly as we need to see the fallout of the Chosen Slayer spell, even if just in exposition. I think it would be a lot more fair for the new Slayer to have some uniqueness returned to her by paring that Slayer count back down to Buffy and Faith first. It would up her importance in her own story intensely.