That's not what OP asked for. You are talking about PC games here and a > $1000 investment.
However, OP asked specifically for a PC to play 3DS games.
Point is: PCs don't run 3DS games and emulators such as Citra currently don't do a good job at it either. Some games aren't nearly fullspeed. So if OP is looking to buy a PC to play 3DS games this is the wrong approach. And making it sound like you have a working solution for a PC which runs 3DS games is simply false - it will set OP back $1000 with a system which is not able to do what they asked for..
Instead OP should get a 3DS if they want to play 3DS games (which they'll need legally anyway for Citra).
I could list a handful of games which won't work in Citra (regardless of speed) and also a handful of games which are too slow even on fast systems.
We can't predict what hardware will be necessary to handle those as a lot of these issues can be solved by better software. However: that's a thing for the future.
PS: An i7 is usually a bad choice for Citra (or many other emulators) because those are usually better at multi-core tasks which Citra won't benefit from. It's usually better to buy a high-end i3 or i5 at a similar price than getting a lower-end i7.
(That's an oversimplication though, this post is not a buyers guide. Just a warning.)