Okay, as someone who has had every singing problem there is, and I think shares your propensity to singing in your throat, I sympathize! I did take private lessons, then last semester I took a singing class with an amazing prof.
What you should first focus on is relaxing your throat. hang over from your waist, knees slightly bent, and bounce and sway a little to loosen up (you'll look like an idiot, but it works like a charm!) and breath. Keep your hands on your lower back and when you breath they should move apart. This means you're breathing properly. Staqnd slowly, vertebra by vertebra, leave your head hanging till the very end. You'll be perfectly alligned after this, which is great (go you!)
Breath again, holding one hand on your stomach and one against your breast right below the collar bone. The top hand should stay still while the bottom hand should move out with your breath. When your lungs fill, they should expand down and out to get the most air, and that will push your diaphragm (which is a muscle that sits under your ribs and sort of divides you in half internally) down, which is why your stomach expands. There isn't really any air in your stomach, but there is air where the stuff down there ususally sits.
Keeping a relaxed throat and neck is vital to good singing. if after singing for an extended time your throat hurts, that's a sign of tight muscles. Yawn, and feel the stretch in your mouth and throat -- that's your soft palette, it should be relaxed. A relaxed tongue is thick and sits against the roof of your mouth. While warming up (which is THE most important thing to do!!! And not just singing the song a few times, work those scales quietly for a while, then you can get loud) hold your hands against your throat with the heels touching in the center of your throat and your fingers wrapped around. it should feel loose as you sing.
There's lots of other things you can do as well, just remember that even Pavorati is still learning to deal with a tight throat! and it won't happen overnight.
* Imagine a line dropped straight through you, pulling you straight from the top of your head (you can even have someone pull up gently on a few of your hairs to get the feeling!) and another line, or axis, through your shoulders which straightens out your torso.
* Keep your feet planted about shoulder width apart and your weight evenly distributed.
* Practice sitting down, on the edge of your chair so you don't slump. Only having to think about half your body makes it a lot easier!
* Try to breathe properly all the time, and it will come easier for singing.
* Hold your chin with your thumb tucked under where you can feel the base of your tongue (swallow to find this place by the movement) Sing like this, to make sure your tongue isn't dropping back or moving too much while you sing.
And don't worry about vibrato or any technique-y thing like that. Master the basics, and those things will come in time. Vibrato is a natural thing, and trying to force it or overly emphasize it without the proper training will hurt your voice.
The book I had for class was Basics of Singing, by Jan Schmidt. It's a textbook, but if you can find it it's a really great basic manual, with some great basic songs.
I hope this helped a little, and just remember to have fun. If you are going into college (I don't know if you're planning on college!) take a singing class if your time/credits allow, it's a great experience, and good training!