It depends on your habits. If you do lots of downloading and create lots of
data then you need a large home partition. If you plan on adding lots of
applications then you need a large root partition. There is no magic ratio.

You can get by on a bare bones installation with 4 GBs, but that is not
advised. You should use 6 or even 8 GBs for bare bones. If you plan on
installing more applications then go larger. Obviously larger is better than
smaller. I have Ubuntu 9.10 running on a 16 GB SD card on my eeePC and it
runs fine. I have even had it run on a 8 GB. On my main computer, the sky is
the limit.

I have never run out of space on my root partition, but I have run out of
space on home in the past many times. I usually allow 30 GBs for root and at
least 50 GBs for home. If you have more space devote it to home because
after awhile ratios no longer apply because you cannot fill up the root
partition past a certain point. If you are limited in the amount of space
then you need to be vigilant in reducing waste. Clean out your caches and
move data off line as needed.

A good utility is Ubuntu Tweak from Getdeb.net. It is better than Computer
Janitor in that it cleans out caches, old kernels, etc.

As for the router problem, I am no expert here. I am lazy or at least that
is my excuse. My son is a network admin so I have never had to do anything.
He set it up once and it has always worked. I know that he connects through
the terminal, but you can connect through the browser, too. I have set up my
wireless connection many times using the GUI.

Here is a good guide:
www.debianadmin.com/...sic-and-advanced-users.html
Here is the Ubuntu page:
https://help.ubuntu.com/community/InternetAndNetworking

I am also sure that some of network gurus here can come to your rescue.