1. No, no, no, no, no. You should actually wait about six months (or at the VERY least four months if you just can't wait) after an initial piercing to do your first stretch. Also, you probably are only at an 18G right now so going to 4G right off the bat would be skipping six sizes; you should never even skip one.
2. Yes, that's fine; titanium is one of the best materials you can use.
Honestly, piercing guns are crap. They fire a blunt object through your ear, most likely giving you scar tissue right away, which is going to make stretching harder. Also, the jewelry they start with is very thin, which means you have to go through more sizes and the stretching process will take way longer. To be honest, if you want to be at 4G as soon as possible, I'd remove your current piercings, let them heal, and get repierced at 6G or even 4G at a good, reputable shop.
Sorry to be lecturing you or whatever, it's just that a lot of people don't realize what a long process stretching is and how much patience it requires. Try reading this guide to get you started:
http://www.bodyjewelleryshop.com/forum/ ... garding-It