I ran a GT 210 on my 250-W PSU, can I run a GT 710 2GB or GT 730 2GB DDR5?

Well due to the CPU being old , i think it's logical to buy a whole new system , but anyway the recommended power supply for GT 710 2GB DDR3 is 300W and for the GT 730 2GB GDDR5 it's going a little bit higher 350 watts would be recommended,but that is assuming that you don't have any PCI modules (modem or lan card or wifi adapter)
at the end i think it's better to put the motherboard and CPU upgrade in the priority.

some points:

1) Do you have 64-bit Windows?
If not you need that or will be extremely limited in video card memory (a 2GB card would only leave about 1.8GB available for system memory since VRAM gets allocated then some other minor stuff then whatever is left of the 4GB memory map can be used by system memory).

If you have W7 or W8 32-bit or 64-bit you can upgrade to W10 for free (though almost certainly need a CLEAN INSTALL for W10 64bit)

2) PSU:
I'd suggest aiming for a $100, GTX750Ti though you'd want a better power supply. You can likely get by with a $40 model on sale. I normally recommend better ones but for budget that's what you have to do.

A GT710 is complete crap for gaming and the GT730 better but not really that good. Some of the GT730's have 96 cuda cores and some 384. A GTX750ti has 640 but is clocked higher so if we ignore any CPU bottlenecks it's about 2X as good.

The GT710 has 192 cuda cores so the GTX750Ti might get 4X the FPS in some situations.

3) GAMES:
a) GTA4 runs like crap on many systems. I don't recommend it. Maybe something like Saints Row 3 which runs a lot better on my system.

b) COD Modern Warfare probably works okay depending on which one you mean. I have I believe "COD 4 Modern Warfare" from 2007.

c) Half Life 2 is an example of a game that's older, but looks great is fun and runs well. You'll need to carefully do your research.

d) Crysis 2 - not sure about the CPU part, but a GTX750Ti should work well. I could get well over 100FPS on lower settings which still looked great.

e) Metro 2033 - probably similar to Crysis 2 but you'd want to tweak the settings carefully. one of the anti-aliasing settings completely kills frame rate (I think it's AA). It's got a benchmark which is pretty handy though probably not completely accurate.

4) 3GB is problematic for many games, so you should run a "can you run it?" page or google the minimum specs. Skyrim with light modding took 1.75GB for the game, and Windows 10 can drop under 1GB when required so you have just enough for that game.

Metro 2033 claims only 1GB needed which really surprises me, though i suspect that would cause stuttering if you only had that.

*you'd want the REDUX version of that, and maybe get both games though it would be nice to know if they would work well before you buy.

**You can attempt to Google a game on Youtube by listing your CPU name and the game, look for a similar GPU, and then look at his comment listing FPS and low/high settings. they should hopefully list the FPS when not using recording software and maybe give a general comment on game looks and playability (often the videos are overcompressed so useless)

The GT710 uses very little power. It's probably around 20W (update: listed as 19W). again though if you look at my very long comment it's not a great GPU and most or all the games you mention would probably run like crap

It's not meant for gaming. It might be okay for Torchlight or even Diablo 3 but Metro etc would be horrible IMO.

as i said it's the recommended power but some times GPU needs to go further and it will need more power to do so , however the real power needed for this graphic is 125W but considering other parts and that 3GB DDR2 ram of yours it' recommended to upgrade but if you don't it will not be a problem however it might go a little risky some times. in common they say further proof the system , so that if you wanted to add some PCI module or upgrade the ram or the cpu you wouldn't need to buy a PSU.

I have personally tried running a GT 710 2 GB with a 250 W PSU. My PC is an HP Pavilion. It was really a pain. I got Blue Screen every while. It's not that 250 W isn't sufficient, but older PSUs aren't that efficient anyway. It's highly recommended to get a new PSU. If reliability isn't a factor for you, you can get a generic PSU for dirt cheap. Else, Corsair VS450 is a reliable alternative. However, if you're going higher with something like a GT 740 or a GTX 750 Ti, you should probably go for a CX430