Price alone isn't really going to tell you much, you still need to know the CPU model and clock speed (along with other specs). Though admittedly you are probably unlikely to find a laptop for that price that would be powerful enough to run Citra particularly well (unless you find a really great deal on a preowned laptop).
It also depends on the game as well, different 3DS games have very different requirements. You could run some 3DS games well even on a slower laptop, while there are actually a couple that can give even my 4670k 4ghz desktop (and GTX 1060) some trouble.
Note that you should also be concerned about how sturdy the laptop is as well. Cheap sub-$400 consumer-grade laptops (such as Dell's Inspiron or Lenovo's Ideapad) you see at Best Buy and other stores are often priced that low for a reason. In my experience, they're generally built poorly with low quality materials. Especially ones with most/all plastic cases. I've had a handful of these unfortunately, all of them quickly broke even with careful and light use (common issues include faulty keyboards, weak hinges, power supplies/jacks and displays going bad etc).
I agree with the above post suggesting an older laptop. You can probably find a used Thinkpad (Dell Latitude is okay as well) with a respectable CPU at a reasonable price. You can often find these pre-owned, some of which are still in good condition due to their relative sturdiness compared to the newer consumer grade brands.