Theres a few things to consider:
Clean installation. Windows XP installations deteriorate in performance as time passes. Clean installation of XP in your current systems state will recover some system performance.
The memory modules will help. I would say 2 GB should be the minimum required to run Windows XP comfortably. I don't think its worth upgrading to the 4 GB as the rest of the computer isn't so powerful.
Crucial.com/uk has the 2 GB kit for £45.59: http://www.crucial.com/uk/store/listparts.aspx?model=Dimension%208300%20Series&Cat=RAM
Offtek.co.uk has the 2 GB Kit for £31.08: http://www.offtek.co.uk/ram-memory-2/dell/dell-desktop-memory/dimension-8300-series/mid27623#nav
I have successfully used Offtek for many Dell systems on many occasions and for such old Dell models it is often cheaper.
I would personally recommend removing your 2 256 MB modules and replacing them with the 2 1 GB modules. I would then clean install Windows XP. To do this follow my Windows Reinstallation Guide:
http://philipyip.wordpress.com/dell-community-forums/
However one thing you should note is that Windows XP is reaching its End of Life in April 2014 for more information see: Windows XP SP3 and Office 2003 - End of Life April 2014.
I personally wouldn't waste any cash investing in solid state drive upgrades, a windows license or graphic card upgrades for such an old model. If you tally the cost of all these upgrades it can get quite pricy.
The lower end Inspiron 660 would be vastly superior to this model in all ways and you can get it for £299: http://www.dell.com/uk/p/inspiron-660/fs
Or consider the higher end XPS 8700: http://www.dell.com/uk/p/xps-8700/fs