According to this website, the recommended requirements for SSF are: So it sounds like you could get any modern "decent" laptop and run it fine, focusing on the CPU over the GPU, of course.
Let me preface this by saying that typically, the thing you should worry about the most when it comes to emulation is your CPU. Your GPU also has to be reasonable, but it's less of a problem I'd say. Maybe surprising, but in the system requirements... ... this line of CPUs really isn't anything special. Just about any modern laptop (and by that I mean most, but not all) will surpass this no problem. And although it was a long time ago now, I had no problems emulating the Saturn on my Intel Pentium 4 (2.4GHz). I didn't play particularly demanding games though; just things like Sonic Jam, Sonic R, 3D Blast, etc. As far as I'm concerned, you shouldn't have to spend more than $500 at most, and will probably end up in the $300 range. I could be completely wrong of course, but that's what the prices were like last time I looked for a laptop for a friend... before convincing him to just build a desktop which he's super happy with now :v: Also, on the note of ripping your games: SSF can't open disc images directly. If you have some software to mount the disc images you rip though (or if you just run Windows 8 and rip your discs as ISO), you should be fine.
Off the top of my head, I'd say Burning Rangers is more demanding than the games I mentioned, but I haven't personally tried it.
I'll tell you one thing; stick to SSF. Yabause is way too resource-hungry, even for my gaming laptop.
A high-end Core 2 Duo can actually run SSF full speed, minus some of the more demanding options (SH2 cache and deinterlacing both put such a great hit that it couldn't run at 60fps on my old C2D e6550). However SSF is extremely multithreaded, so if you grab a modern quad core machine, it will be running it fine with all bells and whistles. A Phenom II x4 could do so at the same clocks as my e6550 (they have the same IPC so only the extra cores helped). A strong GPU isn't required, though SSF does use pixel shaders for some of the internal math. However you could pick up a modchipped, region free Saturn for way cheaper.
I wonder if it would be feasible (and relevant) for a Saturn emulator to take advantage of GPGPU, now that stuff like OpenCL is getting common… Hm.