I'd get a new graphics card. You could get either an RX 480 or GTX 1060 for a bit over $250. Another option is to get an SSD. Depending on what you get you may still have enough left over for a graphics card upgrade.
This goes a bit over budget, but you can get a GTX 1060 6GB and a 240GB SSD for a good price. It's not the world's fastest SSD, but it'll still outperform a hard drive and has pretty good value. You could also get a RX 480 instead of a GTX 1060. It's not quite as powerful, but it does perform better in games that support DirectX12.
PCPartPicker part list /
Price breakdown by merchant
Storage: OCZ TRION 150 240GB 2.5" Solid State Drive ($65.99 @ Newegg)
Video Card: Gigabyte GeForce GTX 1060 6GB WINDFORCE OC 6G Video Card ($249.00 @ Amazon)
Total: $314.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-09-26 22:17 EDT-0400
You could instead opt for a higher quality SSD. You'll get faster read and write times, but it'll set you back more. Your options here for a GPU are the RX 470 and GTX 1060 3GB. The 3GB is weaker than it's 6GB counterpart, but it still performs better than the RX 470. However, the RX 470 has 4GB of memory, which will help prevent stuttering and hitching resulting from the limited 3GB of memory.
PCPartPicker part list /
Price breakdown by merchant
Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($93.88 @ OutletPC)
Video Card: Sapphire Radeon RX 470 4GB NITRO+ Video Card ($209.89 @ OutletPC)
Total: $303.77
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-09-26 22:31 EDT-0400