The website potentially represents you in every way, and it will be seen as part of the application.
If it's professional, it will be to your advantage. If it looks like too expensive though, you may be seen as someone wasting resources, which wouldn't be good.
If it looks great, even if you didn't make it, it shows that probably you'll have an eye on websites that you work on (even if you don't do every bit in person). If it looks sloppy, you might be seen as sloppy.
If it looks super simple but also neat (like academic websites from the 90s), you might be seen as the perfect nerd (which might help if you are one) and as a practical person. And so on.
Bottom line: Each thing you do can be interpreted in a lot of ways, often both positive and negative ones. There's no general rule.
That's why I'd make it consistent with what you're going to represent in the application process. If you're a Java developer, it's okay if it's not super great with respect to its design or mobile-friendliness, but it should indicate that you work carefully (no typos, clean code, general design principles followed that you'd also adhere to in a Word document etc.).
Suggesting skills that you don't really have is unnecessary and can become counterproductive, but even this isn't always so. The greatest website might win the application process, and yet they never ask the winner to do the same for them. It's somehow a matter of luck.
If you ask me, I recommend to stay consistent and practical. My foremost suggestion is that you should like the website and not be shy to present it and that it should be consistent with the job you're applying for.