I want to pick up be able to hold a small metal ball with it
How heavy is the ball?
Have you made sure that the ball can be picked up by a permanent magnet?
Will your electromagnet pick up
anything? Paperclip? Iron filings?
Does the battery warm up much when it's in use?
The strength of the electromagnet depends on the current through it, the number of turns, the diameter, and the core material. Generally the relationships are quite complicated so when you are starting out it is a good idea to keep the geometry as simple as you can. It is possible to work out rules of thumb from there (and looking them up of course).
Have you been looking up the theory of electromagnets?
Have you looked through the many similar questions on PF?
Have you tried following one of the many demonstrations on youtube?
A multimeter is an essential tool for messing about with electronics - you must get hold of one.
The Ohms scale can tell you stuff like if all the turns in your coil are conducting or if there is a short that bypasses a lot of them. A simple continuity tester (battery+wires+light-bulb) ca be used to investigate if there is a short to the core though.
You can also investigate the current through the coil and the voltage across it.
You do want an iron core - and I'd keep a small additional load in series too.
It may be possible to figure out what your coils should be capable of if we knew the dimensions.
Looks like about the diameter of an AA battery, on a hardened steel core, quite a small gauge I guess I could count the turns...