In addition to "Christmas shopping," there's a few normal uses for incognito mode too. I steal free news from the New York Times this way, since they can't use cookies to limit me to 10 free articles. I know, I know, I'm a terrible person and such.
As
@johnnyshinta said, secure folder is a good way to keep your private stuff private. Basically it's a phone within a phone, and nothing inside secure folder can access anything outside secure folder. You actually put a separate copy of every app you want to use inside this folder, and it will never see anything outside that folder. I use it to access my work email and chat services, because my employer's IT policy requires me to give them permission to
wipe my phone if I choose to sign into my email via Microsoft Exchange. By using secure folder, all they can do is wipe the contents of said folder. My company's data also remains secure, since the folder is protected by a separate password. Which is good, since I won't get fired for letting trade secrets get out if ever drunkenly pass my phone to a corporate spy at the bar, or something.
I mention all that to remind you that "phone within a phone" doesn't equal privacy. It's a start, since people who know your password won't be able to access secure folder (as long as you set a separate password), but if you log into your Google account or something, your browsing history will show up on
any device that is logged in to your Google account. Also, once you unlock secure folder it stays unlocked for a preset amount of time, and the default value is 15 minutes. So incognito mode is still a good idea, whether or not you use secure folder. You can even set a separate password for it, and have your own private bookmarks. If you want to talk about deep cybersecurity, remember that technically your ISP still has a record of what websites you're visiting on WiFi, and T-Mobile/Verizon/Whatever knows where you browser on their LTE networks. But worrying about that is probably overkill.
I guess it's a matter of who you're keeping stuff private from. If it's a wife, girlfriend, mom, etc. then I'd say that incognito mode is the way to go. If you're just worried about some Joe Schmoe picking up your phone and seeing your browsing history, just encrypt your device (and maybe SD card), and you're good to go. Like you, I prefer to keep my browsing history private from the outside world, but I don't really care if my wife sees it since I don't celebrate Christmas. So this is about as far as I go.