How lovely to be among so many cloth users and potential cloth users!
OK, it's not for everyone, and this isn't a guilt trip for those who don't fancy it for whatever reason. But if you think you could do a few extra washes a week, have a bit of time to sort and assemble them, have a shelf or drawer to stock them in, and room to dry them, and have the cash for the initial outlay, it's really worth it. It's economical, you don't have bin loads of dirty nappies, you don't have to buy packets and packets of "sposies", and of course, it's green (up to 40% more environmentally friendly than using disposables).
The best place to start is a nappy library if you have one near you. We started part-time (at 10 days), because we didn't have a full turnover of newborn nappies (will buy extra for this baby). Birth to potty (B2P) nappies aren't really birth to potty, more like 3 months to potty. We've been full-time day and night since DS was 3 months (or younger, I can't remember exactly), using sposies on some holidays though.
I'd recommend Babipur as an online shop, they have a great range and excellent customer service. Their Facebook group is worth joining too for "mum chat" and advice. There are lots of different brands and systems, so it can be a bit overwhelming, hence the advice to visit a nappy library. If that's not possible, I'd suggest buying a starter pack of different nappies and trying them out. Secondhand nappies sell really well too, so don't despair if you don't get on with a particular brand. One thing to avoid IMHO are "kits" - brands selling 20 or so of one type of nappy for hundreds of pounds to see you through from birth to potty. Yes, you save money by buying in bulk, but there's no guarantee you'll get on with any given nappy. Babies are all different, different morphologies, amount of wetting etc, and some systems suit some families more than others.
I also did a questionnaire with The Nappy Lady before I started buying any, I'm not sure if she still offers that service, but it was quite accurate.
Always happy to answer any questions you may have - we've tried loads of different brands (because I was curious, not because none of them worked) and systems.
As for gender-neutral clothes, we go for organic and cut-for-cloth brands where possible (quite £££, but the quality is worth it, and have bought loads of 2nd hand), and these tend to have gender-neutral options. British brands: Frugi, Little Green Radicals, Piccalilly, Kite, Toby Tiger, Gecko. Scandi brands: Maxomorra, Smafolk, Villervalla, Mini Rodini, Albababy, Duns of Sweden. Slugs & Snails make unisex tights. Little Bird at Mothercare is also really bright and cheerful, and a bit more accessible!