The following comments are related to machines used to build BridgePoint. For building user models I think I would suggest 4GB as the minimum.
I prefer 16GB, using 8GB for the eclipse executable. However, this is not necessary for normal BP development. You can also only use ~4GB if running with the current product (32-bit limitations). If you have many build iterations and many test iterations you will likely hit an OutOfMemory error, causing you to restart. With the 8GB memory setting for java you rarely need to restart eclipse. As for processor, I do not think we have any requirements. But of course as Bob stated the bigger the better :).
Also note that the work to move BridgePoint to eclispe 4.4 has shown that a requirement is to have java 1.7. There is also another plug-in that requires java 1.8. Given this, soon one requirement will be to have at least java 1.7. Also note that the 1.7 requirement we likely be for building user models as well.