Hp 8300 new gpu

So somebody abadoned a computer (after 3 months of sitting here) that I fixed and I am now the official owner of it.
I now have an hp 8300 elite.
It has a:
i7 3770
4gb of ram (the other 12gb is broken)
no hdd (never payed for the new drive so reused it)
no cd drive
standard 240w psu
pretty busted case(already got new front panel so that at least is fixed).
and all the other hp stuff.

So now here is my question:

I want to upgrade the hp's gpu BUT it has a legacy bios and I know this can have major issues with newer cards.

I know it only has a 240w psu but with gpu and everything benchmarking it pulled 92w. It also kept working fine when I plopped in a gtx 650ti I had laying around here and was only pulling around the 200w mark and still working just fine (used a adpator for the 6 pin).

So I want to know what my best option would be for a low profile card that could work with this pc since I need some gpu acceleration for the applications it runs (preferably nvidia since cuda works better in my case but amd is fine too).

Budget at the moment is around the 120 euro mark but I can go higher if needed.
 
If you have a 650Ti there you had laying around, and it's working, leave it in there, why bother with another card? I doubt you can put in anything faster unless you want to use a 750Ti and it's not really worth the money since your card is free to use.
 


Sorry it's a gtx 650 I put the 650ti in the 650's box and switched them around. It can't boot with a 650ti since it needs too much power and the 650 is not mine so I can't really use it.