Keep in mind that starting any new business requires some up front investment on your part. Not investing any of your money into your business as initial startup cost, it brings question to how serious you are about actually wanting to be in business. If you use a free host, please keep in mind that you will most likely not be able to use a dedicated IP. Not having a dedicated IP means that you will not be able to get an ssl certificate for your business. Having an online store without a signed ssl certificate for your company raises questions from the customers as to how secure your site really is and will make them wonder if they even want to do business with you.
So I think it may be in your best interest to pickup a paid hosting account which also gives you a dedicated IP so you can install an SSL certificate which will give your customers piece of mind. If you want to send me a PM, perhaps I could give you a few free months on hosting at RegisterBird, but you would have to be responsible for paying for the hosting after that.