Since it is mostly for browsing, and given the limited amount of RAM on this computer, I would also go for Puppy.
Puppy has the option of 'frugal installation' which just means that instead of being installed to a partition on your flash drive, it only installs to a directory (folder in Windows speak). So removing the operating system from your computer is simply a matter of deleting the directory. Having a 'frugal' installation would be a dual-boot system, in that you would also run a bootloader when you install Puppy, and would be presented with a choice of operating systems when you boot your computer.
Besides a full installation and a frugal installation, both of which would mean booting from the bootloader on your HD into the USB, Puppy can also be booted directly from USB so long as your computer is capable of doing so, and you can create a 'save file' on the USB to store your settings and any software you installed etc. If your computer isn't capable of booting from USB, another option is to boot from CD into a 'save file' on USB.
Neither of these latter options involve running a bootloader, and you would not have a dual boot menu; if you want to boot into the OS you have on your HD you would boot up as normal, and if you wanted to boot into Puppy you would boot from USB or CD.
In the first instance though, I would download some distros and try them out, if you haven't already started doing so.
Also, whatever Linux distro you decide to go for, and particularly if it isn't Puppy, you would have to create a swap partition or file (which is the equivalent of Windows paging file / virtual memory) on your computer, preferably on the HDD, if you want to be able to do much with it.
EDIT: I have just realised that this computer is a laptop, so you may not be able to set up a dual boot system as I described along with the laptop's original operating system (assuming that is what is installed on it), depending on how the manufacturer set it up. If that is the case, then your only option would be to boot from USB or CD. That is what I had to do when I was still running XP on my laptop, although I eventually deleted it altogether and now have a dual boot system with Kubuntu 12.04.5 and a frugal installation of Lucid Puppy 126.96.36.199.
Edited by Al1000, 18 October 2014 - 05:29 AM.