Question What is the best gpu for a4 6300?

I think you can go for the GT 710, or even the GT 1030. I don't think there would a very huge bottleneck when using the GT 1030, imo ? But bottleneck is kind of subjective.

It depends on which type of game you are playing, and also the screen resolution, and other in-game graphic settings applied. For 720p, I think you should be fine.
It doesn't really matter of the CPU/APU bottlenecks the GPU. This is not something that should be of concern. It won't harm the GPU at all, or cause it to perform worse than a less capable GPU would.

Throw out the word "bottleneck" from this discussion. The only relevant question is whether the new GPU will improve performance.
According to the hierarchy chart, and taking into account cut-down variants of some of the budget cards, in order of performance from lowest to highest:
  • GT 1030 SDDR4 - avoid this
  • GT 1030 GDDR5
  • RX 550-512
  • RX 550-640
  • RX 560-892
  • RX 560-1024
  • RX 570
  • RX 580
Once you start getting into RX 550-640 and both RX 560 cards, though, you find that they equal or exceed the price of an RX 570. Currently in the US, the Sapphire Pulse RX 570 4GB can be had for $119.99. That's the best bang-for-buck you can get with a new card, and, even if it's more than your A4 can keep up with, you can carry that card over to a new system when you upgrade to a new platform.

The RX 550-512 and the two GT 1030 cards are cheaper, but their price/performance ratio falls far short given the discounts on some of the RX 570 cards.