Shooting meth becomes the ruin of a lot of users. For me it never felt THAT much better than smoking. But for some users I knew, it pushed their habit to a different level. Similar to switching from snorting heroin to shooting it.
If you are gonna boot it, don't use your hand. The veins look nice and big, but they have a tendency to roll. Plus there's nerves and littler veins all mixed in there. Not as bad as your foot, but still bad.
Chances are you're gonna miss. No offense. It just happens a lot in the hands and this being your first time....
Missing a meth shot is wasteful and painful. My extensive experience with shooting dope has led me to basically never use my hands. Even if you do hit, hands have a tendency to swell temporarily. Not something you want to walk around with.
Use the tried and true spots. Crook of the arm is as simple as it gets. There's a very helpful how-to in this forum. Be careful with that shit.
Arteries have light pinkish blood. Veins have typical, dark red blood. Familiarize yourself with the "tried and true" area you're gonna use and you should be fine in regards to avoiding a artery. Don't shoot in your wrists, neck, groin, etc....
There's threads in this forum on what to do in the off chance that you do enter a artery. Worth reading up. Shooting into a artery can be disastrous.
I'm not sure how much I can say as far as telling you how you can acquire syringes... With pharmacies in the states, it's just a matter of finding one that will sell someone insulin syringes without a prescription. They're around, but harder and harder to find. What you plan to say is fine, provided they're willing to sell them.
We also have needle exchanges in most every large to decent sized city. Any and all info involving a local exchange should be available online. Those are your best bet. IME, I've always been treated kindly and left well supplied. Not just with rigs but with alcohol swabs, ampules of purified water, cookers, disposal boxes, etc.