In summary, having a website created in WordPress would allow your website to look professional on both laptop and cellphone, and being a first good step for an online presence. Creating your website at the same time as your business by a professional could save you money as most web designer or web agency offer a free logo design with their website professionally designed creation.
With a limited budget, you can still reassure your client and start promoting your business on social media and Search engines and therefore start selling. An email marketing campaign can be built to increase your numbers of possible clients and also increase your direct sales. Eventually, when your business will grow, it is possible to add new pages easely.
On the process of having a website, you would buy and secure your custom domain name and having the chance to have your free professional email address (read how to get your professional email accounts) right from the start.