As a teacher I've been privileged to work at some rather high-income households – a place most teachers would want to find themselves. Whatever proverbs say, you are judged by your appearance. Let's go through what your appearance should be like to fit in these circles.
The trick is – you do not want your appearance to be noticed, or if noticed – it should be just slight positive. Parents minds at such households are far too busy to notice you too much. You should just seamlessly blend in wearing clothes that fit you well and make you look good.
Make sure your teeth are healthy and freshly cleaned with mouthwash before you come, or use chewing gum if it's later in the day. Make sure your skin is healthy and you shower in the morning, your hair and nails are clean. If you come unshaved, you'll be seen as undisciplined. You should be fit too. Needless to say, smoking smell is a taboo. At one household I worked for over a year, I was told the mistress dismissed one candidate who weighed 150 kg and smelled strongly of dog.
You're expected to wear neither high-end luxury nor poor clothes. If you come wearing Off White, the parents will involuntarily notice it, that's the type of lavish youth clothing they might expect their children to wear – not you. And if you're wearing rags you're unlikely to be a good specialist. I wear Levis jeans and Lacoste tops (most of which were gifts), which are premium clothes that fit me well and which are reasonable for me to afford. Sometimes it's H&M with Zara jackets. If you're a beginning teacher and can't afford it – you can still find affordable, stylish clothes and look smart in them. You may want your clothing to look firm and dark, which conveys that you are not a person to cross.
It might come as a surprise, but the colour of your bank card matters too. If you have a premium banking card – gold, black or platinum – that's telling the parents you are a well-off specialist.
The thing I've most often been remarked on was my phone. I never thought it would matter so much, but in high-end circles the iPhone is preferred. Both parents and children alike were surprised with me having a Samsung, despite it being of comparable quality and cheaper, that I decided to buy the iPhone the next time I need a new phone to avoid this unwanted attention.