Since no one else has answered, here's my two cents. Yep I work with computers a lot, but your requirements were similar to mine, (I don't do games). Mine was also getting very old, so I recently went for a refurbed job off ebay e.g. :http://www.ebay.co.uk/itm/WIN-7-HP-Dual ... 1228344556
My spec was different in that it was a Dell and I wanted it to support twin screen, but you get the idea.
In the meantime, assuming you just want a temp fix then yes, for what it's worth AVG is good, I don't think it hogs CPU anymore than a lot of them. Just watch out you don't need to upgrade to the Pro version - which you tend to get prompted for occasionally. Really not needed.
However, if you do upgrade the desktop then if you buy one pre-installed with Windows 7 it has built in anti-virus anyway - they tend to come flashed with a fully licenced version of Windows plus OpenOffice. What I then did was install MS Office alongside this using my existing disks and licence.
My new one works great, allowed me to keep the old peripherals (screens, speakers and printer) - the only thing I bought in addition was a USB keyboard / mouse as my old one used the PS2 connectors (now pretty defunct and shows you how long the old Dell Dimension I had before lasted) - all for 160 quid. Well and truly future-proofed.
All I did was take the side off when I got it, re-seated the disk and copied the old data over via USB drive.
Re laptop. As opposed to the above, I wouldn't opt for second hand. Desktop towers tend to be fairly robust and not exposed to much hardship. Laptops are portable by their nature, so you really can't tell how much abuse they've had. You might get a good 'un, you might not - luck of the draw.
If you opt for a laptop normal ones are not expensive anyway and I'd probably go down PC world and have a look where you can actually physically have a proper look.
I've not much experience with the rugged ones (well, not for a long time back when you had pressure valves on the flight cases anyway). I'd probably just opt to get a good padded bag instead unless you have a specific reason for abusing it.
I'm just here for the gasoline.