what is the best graphics card to pair a core i3 6100 with?

Bottlenecking is not really a problem. It's one of those fake problems that people needn't worry over, like whether one brand of toilet paper is better than another brand, as long as it wipes your ***, they are all just as good.

The i3 has the same single core performance as the Core i5 and Core i7. With that said the Core i3 wouldn't bottle neck the card. The only time you'd see a bottleneck is when you played a game that can use more than 3 cores. So essentially, you would be bottlenecked no matter what video card you have.

Unless you're getting the R9 380 for $100 used, you're wasting your money. Get the RX 480 or GTX 1060 instead.

Get the fastest one you can afford because even if the video card ends up waiting on the CPU, you can always upgrade your CPU later and keep your good video card.

There's no such thing as a good "pair" because some games are heavy on the CPU, and some games are heavy on the GPU. Unless you only play one type of game...