Can my PC be upgraded?

I have a GATEWAY DX4860 PC. Yes, it's a pre-built machine which I bought before I came here. My question is - Which components should I upgrade to make this a gaming PC? Currently I am using a spare Nvidia GeForce GT 630 which plays most games at low quality. 

  

After a some research I think I might have to upgrade the PSU and Graphics Card. Are these the only things needed ? Also, can the old/stock power be and replaced with a better one?   

  

Please suggest any good graphics card (budget - $150 to $200 ). Detailed info of the pc is in my profile.

 

Thanks!

 

It is totally possible to upgrade a prebuilt system. I upgraded an HP that my family bought like 6-7 years ago and it is running incredibly well. 

The PSU will be your main problem. You can get a new one so long as Gateway uses a standard size case. Some PCs, like certain Dells, use a custom case that is non-standard. Just pull off your side panel and take a look at the PSU. Measure it and then you can look online for one that will fit.

The Corsair CX430 is a decent PSU. That is what I used. Enough power for a decent GPU and at $24.00 it's cheap. 80+ Bronze certified as well
Does the $200 budget include the PSU? 

If the existing power supply can be removed, I think you could put another one in it, as long as the existing power supply isn't custom made for that particular system. As for the graphics card, again if you can remove the existing card from the x16 PCI-e slot and there is room for another card, I think you could put another one in too. Make sure there is enough clearance for the card if you're getting a dual slot one or the cooler takes more than one slot which most new graphics cards do. For specific cards under your budget, I would go with a GeForce GTX 650 Ti or an R7 260X.

Thanks for your help. My PC has a standard size case. I pulled off the case here's the PSU - 

 

I unscrewed a couple of screws which seem to be that of the PSU and I think can be removed.

The budget of $150-200 is for the graphics card. I don't have any idea how much a PSU costs but I'm ready to throw $50-60