You won't want to try forcing grease in with a gun because you'll end up damaging the gun, (experience). What you need is something like this:
Zerk-Mate Grease Fitting / Joint Cleaner - Alemite
It would be the first item listed. There's a description of the item there too.
As far as a gun, Lincoln is top of the line when it comes to grease guns. I prefer manual ones as I don't have a whole lot to grease. If you have a huge, or multiple machines, with lots of zerks, then a battery or air operated one might make you life easier.