Winnah5

Can be anything higher (in power) than those if you can get it cheap enough. Example if you can get a GTX950 (or higher) in the same price or lower than 750Ti then go for it. Nothing lower as 750Ti/7850 is an optimal pair with your cpu - lower one and your new gpu will be the bottleneck for the cpu.
One additional thing as you might not now this a 670 is more powerful than 750ti and those you probably could also get cheap.
 
Nvidia gpu power you could say that if you take their number from gtx family as XY0 then
X|Y+2|0 >> X+1|Y|0
what i mean on examples
670 >> 750
660 around the same 750
650 << 750
XY0 << XY0ti

Get a new PSU for sure. @cbigfoot gave you a nice suggestion with that. You can also look at this list if you can get a modular cheaper - suggestion look at tier A and PSU with long warranty like that Seasonic.
 
Getting a RTX 2060 now make zero sense, there is absolutely no point in that if you plan to keep current rig with upgraded GPU for 2-4 years. After that time 2060 could be a bottleneck for new CPU or could just be dead and you would never even use 50% of it's power.

So you need more RAM, ok probably best way is to just buy that in shop as DDR3 should be cheap as it's older gen - 60-70 bucks would get you 2x8gb from Patriot, Mushkin or G.Skill.
Sata SSD is obvious that's why I didn't even mention it. You'll be upgrading psu, gpu, ram quite a bit under your budget so you can spend that 35-50 bucks for a WD Green, Kingston A400, Crucial BX500. Later on when you will be building new rig you can take that ssd and throw it into cheap usb3.0 external enclosure.
 
PSU+RAM+SSD+GPU would on total be around 300-350 bucks from what i see online. PSU will be moved to new rig later on, SSD could be used as external.

I would look at a new PSU especially if its 6yrs old and going to add a more powerful card Personally i really like the seasonic Gold + line Fully modular and 10 yr warranty and can easily be moved to a new build. i tend to use my PSUs for 10 years before retiring.
https://pcpartpicker.com/product/WrNypg/seasonic-focus-plus-gold-650w-80-gold-certified-fully-modular-atx-power-supply-ssr-650fx
 
https://www.amazon.com/dp/B073H33X7R/ref=twister_B07ZQHDR5H?_encoding=UTF8&psc=1 $135 us currently
 
and my 2 cents on vcard is look for a used rtx 2060 or Rx580 yes they may be bottle-necked by the CPU BUT will be one less upgrade to worry about in the future. and when the ryzen 4000 series rolls out get new MB CPU (3000 Series will be cheaper then if you dont mind being a generation behind) & nvme ssd and memory and you will be golden. wouldnt buy a sata ssd if you dont have to.

@Winnah5
Hey,
Upgrading this machine hmmm... I wouldn't. That CPU is old and weak as hell it will be a bottleneck for any modern GPU. If don't want to buy a new rig just yet but feel the need to upgrade GPU then I would suggest getting a used GTX750Ti/AMD Radeon HD 7850 or something a bit more powerful that will still be cheap. 60fps on medium in GTA5 no way with that CPU, maybe 60fps on low.
RAM 16gb with that CPU is not worth it if you don't use memory hungry programs - you won't be using it in new future rig as it's DDR3.