I have a variety of things I use, some more effective than others.
For runs longer than 45 mins - 2hrs for training, I use a Nathan Trail Hydration belt. It has a pouch where I can store an IPhone 5S (it probably won't work with the larger IPhone 6's. I can keep my phone and keys in the pouch and it has a couple cords to tie a jacket to if you start your run early in the morning in a jacket and it warms up.
For runs under 45 min, I typically use a Nathan Handheld Bottle carrier. Like this, but mine is an older model which must have been discontinued.
It has a pouch on the outside that easily fits a phone and keys and adjustable strap and thumbhole so you won't drop it.
I have a couple of other things I tried, and on occasion use, but I don't like them as much as the above 2 items, although some runners I run with love them. Its an individual taste, I guess as to what is comfortable for you. A first is the FlipBelt.
Lots of smaller pockets for all kinds of items such as phone, keys, gels, etc. Put the items in, flip the belt, and they are secure.
Another is an armband that just didn't feel right for me. I have this one from Tune Belt although there are several different ones.
I would recommend going to the local running store. They usually have free group runs on certain nights where you can sometimes borrow a belt or armband to try out and where you can sometimes meet people who will let you try their stuff out sometimes or tell you what works for them. You can also take your phone there to see if it would fit. All of these things are about $30 and under individually, but it all adds up if you start buying things you don't like or won't use, or don't fit your phone, etc.
As for the bluetooth/wireless headphones, I really couldn't tell you. I've been satisfied with just getting a couple pair of regular cheap corded headphones. The cord length is long enough to reach from a waist belt to your ears with some slack.
These work well, are just a little over $7 so you don't care if they eventually break, and they have over 30,000 mostly positive reviews on Amazon.
The most important thing is to just get out and get in the miles and not worry so much about all the gear until you get really into it. Get a good pair of shoes, though.