Is is important? Depends on the business and client base but generally speaking a home office doesn't portray the right image for most serious businesses. That said, until you actually need the space i.e. you have employees who need to be based in an office then there are many other more economical options.
We currently work from home but are in the process of renting a virtual office in a local business centre (i.e. we don't actually have any office space) - cost is around £50 per month to use their address as a mailing address which includes them forwarding our mail etc and then we also get preferential rates on meeting rooms etc so when we need to meet clients we can use the same premises as our business address.
This means we don't have our home address on marketing materials, customers feel more assured as we operate from a business premises but all for less than £2 per day (lots of customers currently look us up on Google maps and comment that we are working from a residential premises) and if we need to do client meetings etc we can.
In 12 - 18 months when we take on support staff and sales we will move to a "proper" business premises but my mantra has always been that when you are starting up keep your costs as low as you can even if you are funded - there is no point throwing money away unnecessarily especially in the early days.
Depends on the makeup of your team. If it is distributed or remote then what is the point other than having some 'head office' location. If your team is from the same area then it is more productive to have a space free from distractions that people can do work and discuss things. If you are working by yourself then you just need to please yourself.