In my experience running out of space is often symptomatic of a lack of attention to the general question of managing the volume of information you are storing. In your example, you've used 30Gb of a partition mounted as / and have 16Gb left in a partition mounted as /home. A short-term fix could be to move some sizeable piece of data to a subfolder of /home from its present location; you may be able to use a symbolic link to maintain access to it. But if you've accumulated (say) 20Gb of data over the last six months, then in four months' time you'll be in trouble again.
I have visited many businesses where the client complains of running out of space on the server, and I have found folders full of photographs of the company picnic or the contents of someone's iPod, usually associated with an employee who long since left their employ. This is the kind of data which can be discarded or moved to other storage media such as DVD.
On the other hand if right now you have a legitimate need for over 30Gb of online storage then a 70Gb drive probably isn't going to meet your needs for very long.
The other point I'd make is that when building Linux servers, it's my usual practice to just have one partition for swap space, and the rest of the drive as /. That way you don't run out of partition space until you've filled the whole disk.