Making bullets on the lathe is fun, like NFG says. If you really want to use copper, get some that is considered (almost) free machining, like tellurium copper, (C145). At least you will be able to turn it without having it come off in sticky gobs, but it still presents a few problems. With some types of copper, milk makes a good cutting liquid. Really.
You won't be able to melt copper for casting unless you have a lot of money for a real smelting furnace.
Brass is a much more suitable material for turning bullets, and it's cheaper than copper by half. You can make twice as many mistakes making your bullets for the same price!
360 half hard rod can be turned to a mirror finish without the grief associated with copper turning. It's the bench mark for free machining metals.
Have fun with your rifle, and enjoy your machining exercises!