Working from home is OK, but you need to have a work space. Treat that space separately from the rest of your home. Don't sit on your couch and work whilst watching your favourite reality show. It doesn't work. For a few hours overtime on some personal projects it's not a problem, but for your regular working hours it's not realistic, or productive, or professional.
If you work from home, set your working hours and in those hours you are at work despite the fact that you are physically at home. Ideally you want a room or area that is your work space and isn't for anything other than work. Separate your home and work life, even if both happen inside your home.
Having a Skype meeting with a client, in your pyjamas on the couch doesn't look professional and is a sure way to lose clients. Having a Skype meeting dressed in a suit in your home office on the other hand, looks just as professional as doing the same in any rented office space.
You don't need to tell your clients you work from home, I don't remember the last time a client asked me about where I work, except for...
You don't need a permanent office space to have face-to-face meetings.
Meet at your clients office/workspace.
Meet in a neutral public place—I have meetings in quiet coffee shops with no problem.
Hire meeting space—Office space you can hire out on a short term specifically for meetings are not uncommon. Lots of venues, hotels, etc. also hire out rooms for meetings. Investigate local venues and know their terms and prices so you can budget accordingly.
There may be free meeting space available, for example at a local library or business center.
It all depends on the specific client and your needs but there are a lot of options.
Interruptions, distractions & productivity
I have a wife and 3 kids.. working from home is hard! If you live on your own it will be easier, but by all means not ideal. I worked from home for years before working in an office and I'm still surprised by how much more work I get done when I'm not at home. There is a lot to do at home that isn't work!
Generally speaking, I get more done working in a coffee shop than I do at home and I get more work done at the office than I do sitting in a coffee shop, but I still do all three. Staring at the same four walls isn't good for creativity, wherever those walls are. So I try to move around, work from home when I can, get out and work somewhere new if I can and go to the office when I need to be really productive.
Networking & communication
I worked on my own, in isolation, for years. Then I moved to an office with another designer and a few other non-designers. It made an incredible difference. It improved my workflow, gave me people to bounce ideas off, gave me confidence in work I was unsure about, helped structure my day (taking breaks together etc.) and it helped me separate my home and work life, which is important for your sanity—believe me.
There are places that hire out office space specifically for designers, so you can work around and with other designers even if you are working on your own.
Networking is important in any area of business and networking from your living room is pretty much pointless. Go out and meet people. The amount of business I've picked up from random conversations with random people is incredible. You don't need to rent office space to network but you do need to get out of your house! Go to events, conferences, whatever is going on, just get out there and talk to people.
I won't go in to any details but think about the costs. You obviously have to pay for any office space you hire. What happens if you can't afford to pay your rent? You also have to get to and from your office, which costs you more money and time.
If you have the space for an office at home are you going to benefit enough from increased productivity and opportunities to justify paying for your office space?