If it were me, I'd probably just get a cheap laptop. You can check a site like Slickdeals to find some rather good prices on cheap laptops. That's the safest bet, but probably also the most expensive.

Generally as a concession to processing power, battery life, and overall space concerns, PDA and other mobile devices don't have support for a lot of the things you mention. Or they may support one but not the other, etc. The PSP, for example, will support Flash, but probably not JavaScript, AJAX, Java, etc... And while the input method isn't quite as bad as you might think, it is kind of annoying.

I would say a cheap laptop is your best bet. Just don't expect too much out of it at the prices some of those things sell for. It will probably work fine as a web browser and word processor sort of machine, but anything much more demanding than that will likely lead to finding out just how ***** the hardware is.

You could also look into small form factor PCs... Bit more expensive, and probably a little more difficult to lug around compared to a laptop, but the hardware is likely better quality in most.