It's hard to go wrong with the Bible app from YouVersion. Plenty of plans to do as an individual and with others, it's been downloaded over 300 million times. I personally like the aesthetics of the ESV app and it's even better if you have the study bible. Both of those are free, but if you want to pay a little the Macarthur app is nice because you can purchase all of his study notes.
Now I don't currently use any of these apps, but they look good. Echo Prayer helps you keep track of your prayers and reminds you to pray. PrayerMate is an "index card" system that I've seen endorsed by several Prayer Prompter looks good because it helps you pray. What I also like about it is it gives you passages to read and pray through.
The Joshua Project gives you the unreached people group (UPG) of the day which I love. Anti-Mosquito Sonic Repeller app is more for missionaries than people looking to learn. I had to include it because I thought it was so cool. It kind of does what it says, it puts out a sound that repels mosquitoes. The International Mission Board (IMB) also has several apps that might be of interest to you.
PS- I have an I-Phone and you should too>.