Welcome back! I also started skating again after 15 years off, just last March. I would actually say to just start with privates. Or at least investigate what the group lessons at your rink are like before signing up. I was back on the ice for about 3 months before I started private lessons, but I wish I'd started them right away. I skated for a few weeks on my own just to make sure I'd stick with it--and a few skills came back from muscle memory. I then signed up for adult group lessons, but while it was technically a mixed level class, I was the only one who wasn't stepping on the ice for the first time. So, I didn't really get any instruction since everyone else was just trying to learn how to stay upright. Meanwhile, more skills were creeping back out of muscle memory, but I wasn't getting instruction on my technique. I started privates in June and that was what I should've just started with--because we've been able to work on skills as they come back from muscle memory (totally out of order, too... jumps before 3-turns, haha), work on new things, and correct bad habits and poor technique that was developed the few months I was skating unattended (it does not take long at all to learn bad habits, haha. Ugh).
So that said, if you can afford it, you'd get the most out of privates. Really getting something out of your lessons will also make you want to stick with it. However, if your rink offers true mixed-level classes where the instructor goes around and spends time with each student--with whatever you're working on--that might be a good, inexpensive way to dip your toes back in. Before committing time and money to group lessons, I would just ask around and make sure that they would really be beneficial to someone who has skated before. Because even though it'll sometimes seem like relearning things takes forever, skills will come back out of nowhere and it'll be exciting and you'll want to work on them.