Agreed. You do not need a powerful computer. If you are in the market for hardware, I would suggest external hard drives for backup as you will need to backup your site and contents routinely if you decided to run the site on your own hardware. Since you are most likely to run the site from a webhosting company, I would suggest you spend some time and research web hosting companies and compare rates and features. If you are planning on running your own hardware for your business, I would suggest you look at Dell's Server sales site.
As for designing, I would suggest taking courses in Adobe Dreamweaver. I would recommend you look at content site managers and/or e-store software if your business sells any products.