Posting your PSU (wattage included) and case is also essential. We need to make sure your PSU can handle the new card and that your case can support the card (for example drive bays in the way or if certain cards are too long for the case, ect.) Another thing, I know you mentioned you won't be getting it soon, but that would be your best bet for the GPU(s) in your price range; reason being is because they might be on sale now but won't be in 2 weeks or any other unforeseeable scenario.

TaigaAisaka wrote Posting your PSU (wattage included) and case is also essential. We need to make sure your PSU can handle the new card and that your case can support the card (for example drive bays in the way or if certain cards are too long for the case, ect.) Another thing, I know you mentioned you won't be getting it soon, but that would be your best bet for the GPU(s) in your price range; reason being is because they might be on sale now but won't be in 2 weeks or any other unforeseeable scenario.

Thanks further details have been added.

Maybe the likes of an rx 460?

Ryan_Reynolds wrote

TaigaAisaka wrote Posting your PSU (wattage included) and case is also essential. We need to make sure your PSU can handle the new card and that your case can support the card (for example drive bays in the way or if certain cards are too long for the case, ect.) Another thing, I know you mentioned you won't be getting it soon, but that would be your best bet for the GPU(s) in your price range; reason being is because they might be on sale now but won't be in 2 weeks or any other unforeseeable scenario.

Thanks further details have been added.

You might have to take your case apart and look at the PSU. On the Amazon page they don't mention the PSU (typical for prebuilt PC listing) and apparently one user said this:

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Edit: Also it would be good to say what games you are trying to play and at what resolution. I'm assuming 1080p, but just to be on the safe side.

You're options are a GTX 1050Ti or a GTX 1050. The reason to get a GTX 1050 over the 1050Ti, would be if you wanted a PSU upgrade as well. Which, you absolutely 100% should upgrade PSU at some point since I guarantee your current unit is terrible, but it should be fine for a 1050 or 1050Ti since they don't need any power cables, just the 75W provided by the PCIe lane.

So, here's the cheapest 1050Ti;
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or 1050;
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and PSU;
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RX 460 makes no sense now since the 560 is out and is basically a fully unlocked RX 460, plus the GTX 1050 is still better than even the 560 anyway.

GTX 1050Ti>GTX 1050>RX 560>RX 460.