That's a really crappy power supply unit. Has two 12V rails one with 10A and the other with 13A... one will be dedicated for the CPU and the other for the GPU probably.
Being a junk PSU probably means that it will output less than what's labeled on it.
Before upgrading your GPU, you really need to upgrade that PSU.
Here's what I'm recommending:
PCPartPicker part list /
Price breakdown by merchant
Power Supply: EVGA - SuperNOVA G3 550W 80+ Gold Certified Fully-Modular ATX Power Supply ($69.89 @ OutletPC)
Total: $69.89
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-11-03 17:37 EDT-0400
As for the GPU the 1070ti is a great deal right now.
Because you'll be upgrading the PSU and your budget might be low a RX 580 8 GB will be a great alternative to the 1060.