As @bobbybouwmann said, start off with a framework such as Bootstrap. To make things a lot easier and nicer in the long run, instead of using compiled assets, compile them yourself and learn SASS. It'll make things much easier :) There are other frameworks, which can do the same plus more, but start with Bootstrap to get the idea how frameworks are built, and how to use them.
The next step is to look into the flow of users around your site(s). It all adds up to make a well designed, well thought out site. Consider who will be using the site, and how they'll use it. For instance a car dealer site would differ in user flow to a corporate site.
Look at adding in third party libraries to enhance the design. A lot of frameworks will have most things (Like modals, tooltips etc) but when needing more complex things like graphs then a third party jQuery library will be helpful.
Work smarter not harder - by this I mean use DRY code. Again, most frameworks will have your back here, but basically, you have one class with common CSS (Such as a class of mt-3, to add margin-top: 3em;) and use it on multiple elements.
Minification is a must too. A design is just part of the user's experience on the site. Minifying files helps reduce load times, and with the help of plugins from task runners you can even remove unused CSS you may not have noticed is there. Also great when using a framework!
Learn about typography! This is a very important step. The right fonts, font weights and colours help set the tone for the site. A corporate site would have a different set of fonts and what not than a kids play house or something.
As you've already mentioned, think simple. You don't need to go over the top with animations, effects, big bold headings etc, just something easy on the eyes, and well laid out.
Content is another key thing. Don't mislead people, and don't make things sound like a scam. Spelling mistakes can put people off, as can bad grammar.
If you leave a link to the site (I know sometimes you can't) we can give you more specific guidance for the project you're working on to make it look less scammy :)
GL with the project :)