Help me choose a new, cheap GPU that will run DBO just fine

My Ati Radeon HD 4550 died a few weeks ago. It could run DBO pretty well but around platform and very populated places the FPS would go way down. Stuttering and lag appeared.

I was thinking between Nvidia GT 710 and 730 but apparently they are meant for PC's that don't have an integrated graphics card... Meaning they are bad for gaming even tho they are both faster than my current dead GPU. I am not a gamer, I am just looking for a GPU that will run DBO and League of Legends decently... Around 60FPS. The 4550 HD ran League on 60FPS +, until recently, before it died it was struggling to get 60FPS.

My power supply is 450W

My PC is almost 10 years old:

Dual Core E5200 2.5 Ghz;

3 GB DDR2 RAM;

Ati 4550 (dead);

Windows 10 64bits.

I could easily buy a new PC but I am saving money for studying and moving out next years plus I wanna use my old PC for another 2-3, maybe 5 years or leave it behind for my brother and parents.

Here are pictures of my display with my current GPU (I had BSOD because of it not long ago, then I changed the thermal paste and it worked a few more month until this happened):

But without fps drops at crowded places like the platform?

The 1050TI is around 170-200 Euro's here;
The 710 GT and 730 GT around 50-60 Euros;

The AMD cards are all 150 + Euros, I always thought that they were cheaper....

The 1030 is around 100 Euro's...

Around 10.000 to 11.000 RSD while the 710 GT is around 5.000 - 6.000, might be better to spend a few bucks more I guess? I'll think about it.

Next question is, would those cards be an overkill for my CPU & Setup since its an old computer, Would the CPU make the GPU throttle or the other way around?

Anyways, thanks for all of your replies guys. I've read all of them and I am considering them, I didn't ignore any of them!

Quote from Sendoku

LMAO i had the same PC and could run dbo just fine enough to win budos but fps is trash

i just built a cheap one tho, for best GPU i suggest you a radeon rx 550 it's pretty good (much better than gt 730) for about 90$, though it might bottleneck... other solution is also spend an additional 60$ for a pentium g4560-g4600 which is much better than what u have, tho you won't b able to overclock but it's not a problem for dbo

The Rx 550 is around 150-190 Euros here and if I wanted to change the CPU I'd have to change my motherboard too...
Thanks for the suggestion tho, I've decided to go with a GT 710 2GB GDDR5 card, it's 70 Euros but should be faster than the GDDR3 and DDR3 versions (btw are GDDR3 and DDR3 the same type of memory in GPUs? For example I am starting to think that some websites write DDR3 instead of GDDR3 in the cards specs)

Quote from 2pro4u

I think you should check this out.

. You could get an incredibly cheap pc that can run the latest games at 60+fps at 1440p.

Thanks but the economy differs in my country and I don't really need a new PC for now.