You want a PC that runs modern games at high frame rates for the next five years. To do that, you need to buy once and buy right. That means ignoring the absolute newest graphics cards on day one and looking at last year's high-end models instead, which usually see steep discounts when the new stock arrives.
Timing this build for the November sales is your best bet to hit an $1,800 budget. If you use the Discover it® Cash Back, you can spread that cost out over time without paying extra for the privilege.
Just remember that 15 months is a hard deadline, not free money. If you still have a balance when the 0% intro APR for 15 months on purchases and balance transfers ends, the remaining amount will start racking up interest at the standard variable rate. Pay it off on schedule or the deal falls apart.