So one meal would cost: a bag of microwable rice 59p + 250 ml rice milk 25p + 50 g raisins 15p - in total 99p for the meal. I challenge you to find something cheaper and more filling using meat/eggs/dairy.
Potatoes, rice and beans are the cheapest foods that you can buy, period.
Take it step by step if you can't go full vegan immediately. Eggs have more cruelty associated with them that milk, so are a good start. Over time, you can convince people more and more.
If you are not living with your stepdad, you don't need to convince him. Just try to work on your Mom and Dad. Find a few short videos showing egg and dairy industry cruelty.
Offering to cook some of your own meals (or for everyone) will help.
Re health of a vegetarian diet and your uncle, explain that they should not judge on one person and explain that studies have shown that vegans have health advantages such as lower cholesterol and heart disease, with no known disadvantages. Ask them if they know of any studies showing otherwise.
Well done for thinking through these issues at such a young age. I was not smart enough to do it at that age.
For food, try rice/beans/potatoes/pasta/chips + vegetables for a vegan meal. You can explain you don't need special foods too often, although an occossional soy burger is not a bad idea.
Well, if your animal products are getting to a very low amount, you can consider taking a B12 tablet. If you become a strict vegan, it is certainly reccomended.
You need a source of Omega 3 which can be chia seed, flax seed or walnuts.
Iodine is a tricky one. You can check if there is iodine in the salt your family uses. I also eat cranberries and strawberries for iodine. It can be low on a vegan diet and many articles you will read miss this one out, but it is absolutely in the top three important things vegans are most likely to be low in.
The above three are perhaps the only three things which can be particularly deficient in a vegetarian or vegan diet. If you eat a well balanced diet to include legumes, grains, vegetables (including green veg) and fruit then everything else should take care of itself.
Maybe calcium is one to think about - almonds,orange, bread, broccoli are some example sources, but it does help to have some food (such as vegan milk) fortified with calcium as it can be low on a vegan diet.
Apart from the above advice, assuming you are healthy and have no particular allergies/conditions etc that you know of, there isn't really any need to go much deeper than that.
Also, there is no urgent need to sort all this out instantly, you can work the above things steadily into your diet over the next few weeks perhaps, or months even.
If you want to look into nutrition in more depth, you can look at http://www.veganhealth.org/ and its articles, it is well respected. However, don't think you don't need to understand nutrition in huge depth to be a healthy vegan. It helps but I think just reading the advice in my post and following it covers the basics already to make you healthier than the average meat eater.
Let me know if there's anything you need help with right now. I will try and help you if I remember to come back to this thread.
Yea picking out a few good/short videos maybe on YouTube is a good idea. I recently showed a video to couple friends of mine was Vegan Activist on his home page shows 11min video covers pretty much everything reasons for being Vegan and why eggs and dairy are equally as bad as meat.
Good luck and mind your in the right on this just do a bit of homework and hit your parents with the facts. Sounds like your parents are already on the way to being Vegan they just need the extra info.
Good to hear your update. People that are hostile to your veganism may need time to get used to it, don't give up. Stay polite, and be positive, be insistent. If necessary you can transition first as mostly vegan then strict vegan. Good luck and keep us updated or let us know if you have any questions.
By the way, are you a birdwatcher? There are some nesting birds in our garden.