This app was mentioned in 6 comments, with an average of 2.83 upvotes
They have the license to distribute it in english. Also the app has hardcoded subtitles.
There's the Shonen Jump Plus app, go download it here: https://play.google.com/store/apps/details?id=com.access_company.android.sh_jumpplus&hl=ja
The Shonen Jump Plus manga provides free legal japanese manga.
「劇場版「ドラゴンボールZ 復活の『F』」公開記念だそうだ。
少年ジャンプ+
http://plus.shonenjump.com/
iOSアプリ
https://itunes.apple.com/jp/app/shao-nianjanpu+/id875750302&mt=8
Androidアプリ
https://play.google.com/store/apps/details?id=com.access_company.android.sh_jumpplus&hl=ja
Japanese shounen jump still have physical copies and so does almost every other manga magazine. Easiest way to subscribe is to the digital copy via their app [iOS][Android], 300 JPY per issue or 900 JPY per month.
Physical copies are sold on Honto but they get sold out same day as they are released. Personally I would recommend to go for tankobons if you want physical copies instead as they are higher quality and are cheaper to ship.
You can buy all chapters of the coloured manga from the Japanese Shonen Jump app on Android.
The presence of furigana depends on the target age group of each manga publication. The more furigana you want, the more you have to look for manga targeted at a younger age.
As for reading raw manga in general, assuming you are not located in Japan (otherwise you can pick up any number of cheap volumes at any combini) I can recommend the following 3 resources:
As always, the Japanese publishers are being asses, forcing Google to region-lock their apps so that you can't download them unless you are physically in Japan. Clearly some companies keep their behinds firmly planted in the former century and don't understand the Internet. In any case, you can install the apps from alternative sources and then most of them just work. I recommend installing the APKPure app and then using it to install and update the Japanese apps.
BookWalker is an exception: it will gladly sell you any manga or ebook ever published in Japan and let you read it on your PC or any device you want, through their app, which is why I placed it at the top of the list.
Finally, I included Comico because it's a "webtoon" app, meaning its titles are designed to be read on a narrow screen, scrolling upwards, instead of large paper pages like in Shonen Jump and most other publications. On the other hand, it's difficult to find furigana in Comico's titles.
All three resource have tons of free reading material (look for 無料, free) sometimes just the first few chapters of a manga, other times entire volumes. If you want to read an entire story though, you will have to pay the actual price or subscription. Again, BookWalker has no problem accepting foreign readers and their money. I cannot vouch for the other platforms.