Paid hosting is better
There is nothing called a "free lunch". The provider who does give you free space will employ some tactics to get money back on his free hosting effort. First and foremost is the use of Online Advertisements on your website. If any of the visitors to your site click on these adverts the ISP gets paid for the clicks, not you. The more visitors to your site, the more likely that they might click on ads, and hence more money earned by the ISP. These adverts may be annoying to you and moreover you don't have any control of the content that gets displayed. You may want to avoid this and instead actually buy the space to host your site, and then display adverts of your choice and get paid for it.
Credibility
Why do we step in to the showroom of an authorized dealer to buy certain goods rather than believing a salesman at your doorstep? Simply because an authorized dealer of a company has more credibility. We can put our faith in him and be assured of a genuine product and get service after the sale. Likewise people will not have faith in you if you don't have a place of your own.
Technical Support
With somebody providing you free space, you really cannot expect much in terms of technical support. Moreover the ISP is NOT obliged to look into your problem since you NEVER actually bought service from him. A downtime of few hours could be ok if you are hosting a family or hobbies kind of free website. However, if it is a business website, it might mean losses to your bottom line with a dent in your credibility.
Storage
Free websites will give you space which would be enough for few pages of content and very few pictures if any. This might be limiting especially in case you are serious about your website and working on expanding it.
Ecommerce
If you have a business plan in mind and you are willing to sell your products to customers worldwide, your website must have host of features like accepting credit cards online, ability to add or modify content quickly anytime, include features like online chat, discussion forums and more. This would not be possible in a free website.
Email
To add further to the credibility of your business it is important that you have a business email. This could be in a format like info@yourbusiness.com. A free website might not provide this. You can very well understand the impact of having your own email address in your business card.