Hey B

First off welcome to the forum! It's awesome having you here and I'm really glad that you've managed to work out your feelings and sexuality and starting taking steps toward living the sort of life that you want and need for yourself
That's a really big deal! Many people - myself most definitely included - didn't have any idea about these things when they were your age! I don't think you're too young to have worked these things out at all, and as I said I'm really happy for you and proud of you!

So your parents...yeah that sounds tough, dude

What are their general attitudes about homosexuality and GLBT issues? This matters because there's more than one way to 'want to seem perfect'. A family like that may be extremely disappointed and negative toward their child's coming out if it seemed to shatter their perfect image; however, it's also quite conceivable that your parents would feel like being anything less than accepting and supportive would tarnish their image. It really depends on how they view homosexuality and what they consider to be an appropriate 'perfect' reaction.
Next, let me be a bit optimistic here. Obviously I've never met your parents and have no idea what they're like beyond what you've briefly said in your post; however, there's every chance and likelihood that they love you a great deal and want the best for you. Just because they dote on the pets doesn't mean they don't love you. In fact on the bright side it shows that they're affectionate, loving people. It could be that they're simply more comfortable expressing affection for their pets than they are expressing it for their children. That's sad of course, but definitely within the realm of possibility. Relationships with pets are far simpler than relationships with other people and you never have to worry about rejection or embarrassment from a pet; the same can't necessarily be said about people. I'm reminded of a show I saw several years ago on TV. The father was comfortable saying 'I love you' to the dog, but had an inability to say it to his son. He loved his son very much though, he just couldn't say it. So all I'm really trying to say here is that your parents definitely need to let you know that they love you, but just because they're not good at expressing it doesn't necessarily mean that they don't feel it.
Regarding your new classmate, I'm pulling for you, dude! But do you have any reason to think he might be gay/bi? Or is simply that you're attracted to him and interested? I hope this doesn't depress you or disappoint you, but while the times are changing quickly on this score, you're in the minority of gay/bi people your age who have already worked it out and accepted it. Most people you know your age who really are gay or bi are not anywhere near having figured it out, accepted it, and being ready for any sort of a relationship. So even if he is gay, and even if he does have feelings for you...it might not be that simple; he may just not be ready yet, in fact I would speculate that chances are that's the case. Unfortunately, I also tend to counsel against dating guys that are more than a couple of years older than you, particularly at your age, so if you want my honest opinion I'd suggest resolving yourself to waiting a couple more years before you have a boyfriend.
However, as I said, I'm pulling for you and by all means go and make a new friend if you can! More friends never hurt, even more cute friends

Just accept that he might not be able (either because of his sexuality or simply because he isn't ready) to return your feelings on anything beyond a platonic level. If he is though: Great!

Don't worry about being shy; lots of people of shy! You'll be fine on this score, just please try to be as receptive and friendly as possible when people do make a move and start talking to you/interacting with you

Regarding your friend, I'm very sanguine about your chances of having a good coming out experience with her! It is one thing to have casual gay friends and another thing entirely to have a gay best friend...but I still suspect that if she's genuinely okay with gay people then even if she is surprised by your revelation, and even if she does need some time to process it, she'll come around soon enough

Just give her time to deal with it. In the end she'll likely conclude that if she can be supportive of her casual friends she can certainly be supportive of her best friend. So yeah, I personally would encourage you to consider telling her. Just be sure that you're ready and also be sure that she's not going to tell anyone else (otherwise be ready for the consequences if she does).
Anyway, good luck dude and welcome again

-Kevin