This thread 
My parents (and then, my in laws) are part of the black tie 'circuit.' I've attended dozens of them as an older teenager and adult over the years. My in laws often give charity black tie events. I've attended old school, formal ones because of my work, and family/friends black tie.
There are some odd replies on this thread, and posters keen to stick the boot into other posters for not 'getting it right.' I'm not keen on all that, so I'm not joining in with it.
OP, if you want to feel comfortable in a fitting-in sense (I'm being guided by your thread title here), wear a formal but simple-ish dress, not short, dark in colour, not too tight and not revealing cleavage/slashed to the thigh. Not acres of spangles (although some do a little sparkle). No ball gowns. No one cares about arms btw, so sleeve or no sleeve, up to you.
As it's a black tie hosted at home, I've seen plenty of people bring a small gift, but that tends to be from people who know the hosts pretty well. A card afterwards is perfect.
For the record, people break 'the rules' all time and no one really bats an eyelid. My MiL can be a bit of stickler, but even she wouldn't dream of 'raising an eyebrow' at someone for committing some sin such as bringing a bottle of Champagne or something. I remember a new girlfriend of a BiL coming along to her first black tie hiding behind a vast bunch of tropical flowers and carrying a really strong French cheese
. It was lovely. Another BiL forgot his tux and wore a work suit.
Debretts is hardly wrong on these things, but it's 2021, we're a year into a worldwide pandemic and people tend to be civilized and warm at these things. If they're not, it's because they have fallen short, and not you.
Have a lovely time, OP!