The first step in creating a good relationship with Mum and Dad is accepting who you are today. Acknowledge what was hard about your childhood, and let go of anything you feel your parents "did" to you. You are who you are, for better and for worse. The blame game is over.
When you're going through this process it will help to realise that your parents, too, are the product of their own growing up experiences, just as your kids will be. Yes, there are bad parents out there, but most are just trying to do their best and have no idea what the results will be.
As an adult, you have power over your own life choices. You also have the power to change your interactions with your parents so they're enjoyable, not just obligatory.
There's a temptation (once you move out after school) to only phone home when you need help - when you're in personal, financial, or even work-related trouble - and you don't know where else to turn. Don't make these things your exclusive rationale for dialing your childhood landline number. Phone or visit your parents when you're happy, when nothing is going wrong, and when you're wondering how they are doing.
Also, parental friendships are strengthened when you actually take the relationship out of their house. When was the last time you invited your mum and dad to dinner at your place? Or met at a café or restaurant that was convenient for both parties to get to? Much of the tension between parent and adult child is situational, and changing the physical location does a lot of good.
To a degree, you also have the power to steer the conversation in a positive place. Avoid poisonous topics that you know cause angst, and always go unresolved - no matter how much you talk about them.
Instead, find out new things about your parents. Believe it or not, they had a life before you, and now you're all grown up they have a life after you too. You might even find yourselves bonding over a previously-unknown shared love for Moroccan food, or war history, or marijuana.
Ask for advice only when you really, really need it. It's likely you have other people in your life that can help you with major decisions (and often you already know what your parents are going to tell you anyway). Also refrain from asking for help with administrative duties (e.g. your taxes and your dry cleaning), and don't complain about your siblings to them. All of these things that need to stay in the past with your former parent/child relationship dynamic.
When you're an adult, your parents can start to feel like your equals, not your superiors. It's okay to remind them that you're an adult, but do it gently. In order to dissuade your "inner child" from coming out, know the time limit on your parental communication - for some it will be two hours, others it will be two weeks.
Judgement, or perceived judgement, is something you'll always have to manage when developing your relationship from parents to friends. There will a tone in dad's voice or a purse or mum's lips and you'll just have to let it go, and not let aggregate you. Their judgement might be a projection of their own issues. If you wouldn't let it get you down if it came from a friend your own age, don't let it affect you know.
Above all, don't let any issues fester. Have adult-to-adult conversations and deal with problems frankly and with honesty - nothing will make you seem more "grown-up" and encourage the respect any friend deserves.