It is absolutely fine to employ a web start-up designer, but remember it is a gamble. The new web designers are talented, they know to use the new tools with ease, but they do not have experience or a track record. Keeping that in mind, it is smarter to consider hiring a web designer with enough experience.
Hiring an experienced person for your website design means you can ask the designer to show their past clients work and also their portfolio. There is no need for a portfolio to be flashy; instead it can be a collection of links showing that the designer can do.