I've bought from north shore care before, and when they sent my ATNs, they came in a plain brown box with a small label that said NSC - and then where they were located. I don't know if everything they ship goes out that way, but you may be able to contact them and make sure your order is shipped discretely.
To be more on point... since the obligatory "Check the Wiki" was as ineffective as I thought it would be... I've never really liked Tranquility. They just didn't fit me that well... weren't that comfortable.
ATN - My favorite for being discreet and comfortable fitting. Bambinos for the way they wrap around the sides and prevent side leaks.
With the ATNs I tend to use packing tape on the sides to pull it tighter and reduce the noise when I walk, etc. Then plastic pants can also help with side leaks and reducing noise. Side leakage due to lack of side material is why the Bambinos are what I am using now. No need for plastic pants with the Bambinos.
NSC had discreet shipping last time I ordered. Would order from them anytime. On Amazon I thought I was ordering from them, but it ended up being National Incontinence Supply(?) who sent it less than discreet to a relatives house I was visiting - not happy about that. Luckily mom already knows
I've worn ATN's in almost any social setting without worry. I cut the extra material on the back so they ride lower (won't show if I bend over) and cut material off the leg gathers to cut down on noise.
Darkfinn has issues with the way they fit. I've found them to fit my frame the best out of any store brand or high end brands (I've tried many).
Your fitting and preferences will determine if ATN's are for you. They are my favorites. The peachy backing absorbs well enough for a couple of wettings, but there are others out there with better capacity.
Have fun trying to find the perfect fitting diaper. Once you do find the one you like, order a case!
The mediums fit me fairly well. No elastic waistband is a downside.
I however did buy two bags of the large size, the only difference I can tell between the mediums and larges is that the larges fit like I'm wearing a garbage bag, and they come halfway up my back. Yet there is practically the same amount of absorbant in them as the mediums.
Don't get me started on the tapes. Those little blue "adjustment" squares do NOT allow for great refastening very well at all. One little smidge of finger oil on them and they pop off without hesitation.
Comfort wise. Probably the softest diaper I've worn. Hands down.
Pretty good on leaks, but they are a "half-day" diaper. Can be super leaky if they are not on tight. Well as tight as those blasted tapes will allow.
People that like Molicares seem to appose Abena, similarly if you like Molicares you'll like ATN's since they are about the same pattern and tape placement. Fit is very similar between the two only the ATN's are a little lighter, thinner, and looser than a Molicare Super Plus. They make a very good daytime diaper for me where I don't want to be squeezed around the waist too much and I'll be moving around. Plus they allow me to fit in some of my tightest pants. If I wasn't in cloth I'd prolly go back to ATN's in the day and Moli's at night. And the price point is wonderful.