In my own acquisition work, I found that not having a means of setting up interrupts or other means of Real-time response made for a bad time. I could pipe a lot of data very fast in a burst, but not at reliable intervals due to linux not being a RTOS.
"Real time" is going to be something of a snipe-hunt here because we don't have any actual information or context on the problem you're attempting to solve. I can technically attach a 2.5GSPS ADC to the thing, but won't get 'real-time' throughput on the thing. I could glue on a 1ksps ADC, and to very-much real-time work with it, if my signal processing is simply running a 64 point FIR filter. Knowing what you want to do is going to be far more useful than getting all the numbers of specs of the highest-end X possible.
Right, this is why I recommended the OP look into a BeagleBone Black. The TI OMAP (or Sitara or whatever they're calling it this week) has two onboard sub-processors, which they call PRUSS (Programmable Real-time Unit Subsystem).
The PRUSS is composed of two PRUs, which are essentially little MCUs with direct access to the main CPU's I/O, a shared memory buffer (between both PRUs and between the PRUs and the CPU) plus dedicated interrupts. Each PRU is a custom 32-bit RISC core that can complete most instructions in 1 to 2 cycles.
When the BBB first came out, there was basically no information on the PRUs available, aside from a couple attempts to reverse engineer it and create a compiler from scratch. Fortunately, about two years ago TI released a bunch of information on it, including the official assembler package.
As of now, the assembler is very mature and works well; there's also a cross compiler available so you can program them in C! Once you enable the PRUs via a Device Tree Overlay, they can be programmed right from the command line, which is pretty slick.
There's also a few libraries available that grant you high speed GPIO/ADC access from C/Python/Node.JS/etc. via the PRUs without actually having to write code for the PRUs! (See: libpruio)
The takeaway here is that the PRUs allow real, hardware based realtime control from a non-realtime OS. The PRUSS can read/write GPIO at the main CPU's bus speed, which is 200MHz. If you combine that with an external parallel 8/10/12-bit ADC, you could certainly do some realtime sampling.