An all in one computer is no different than any other computer except that the CPU is built into the display box and it is much more difficult to upgrade individual components.
You need as much display room as you can afford so you can look at all the different windows.
You need as much memory as you can afford to give the digital processing room to work.
You need as good a sound card as you can afford for obvious reasons.
You need as much hard drive space as you can afford so you can record the spectrum for later analysis.
You need as high speed CPU processor as you can afford to allow the software to perform at max efficiency.
Help? Probably not. The RSP2 can work on almost any system. Just like any radio system though, the more you put into it, the better the results you will get out.
If all you can afford is a 19" i3 with 8Gig on the board and a 1T hard drive, it will work but don't expect the performance you can get with spending more on better equipment.
The smart-car will get you from point A to B.
An Expedition will get you there with your family, all the gear needed for a weeks stay plus the boat.
You can buy an Refubish Server here in the German Speaking Area is a Company who sell them quite cheap ~300€ for a Dual CPU Model and 4GB Ram cost ~6€ so...
Maybe that is a better option for you?