I thought about using an RPi for my screener, actually. I use them for all sorts of stuff. I got one set up as an MP3 stereo, one set up as a chart plotter for marine navigation, one as a very portable computer with an ethernet port. They are a lot of fun to mess with. The problem for trading is the graphics. Graphics are verrrrrry basic and you want high resolution and lots of real estate for trading with for instance Trader Workstation, IB's platform. You don't need blistering speed or umpty troglobytes of RAM and a processor that runs at Warp 9. It is nice to be able to support multiple large monitors, though.
Keep in mind that your choice of desktop trading platforms will be severely limited, too. Raspbian, the usual operating system for these little boards, is a stripped down Linux. You can probably run Ubuntu, or Debian, but you will want to use a very simple desktop. A RPi doesn't IMHO have enough muscle to run a VM very well so no WinDOHs. You could maybe try ReactOS which is still in Alpha but I don't have much confidence that you can run a Windows desktop trading platform on it at this stage of development.
If you want a cheap trader machine, get used, or a refurb, or a return. Or a clearance item. Open box. If you have one that is just old and slow and in the way, you could install Ubuntu on it, and run TWS and presumably ToS but no other platforms will run natively on Linux and I wouldn't trust Wine or VM with something like that that could cost you money.