What graphics cards can i put in a Lenovo m58p small?

I'm gonna write this kinda like a greentext.
>be me, a year ago
>get a cheap, but okay pc for $100.49
>Lenovo thinkcentre m58p small with a core 2 duo @ 3.0 ghz, 4gb ram
>pretty happy with it

>be me, now
>get new monitor
>is 1080p
>my computer is now super slow from the high resolution, can't even run Puyo Puyo Tetris anymore
>roblox is even slow

What graphics cards can i put in it? It has small card slots so I can't put much in. If you can't think of one, what about a PNY GeForce GT 1030 (part no. VCGGT10302PB)?

You would have been better off with a used minitower 2nd or better 3rd gen i5, 8gb ram that usually takes a standard power supply.

i5-3470 score 6712, Core2 Duo E8400 @ 3.00GHz score 2149

with over 3x the cpu, double the ram at higher speed, and easier to upgrade, the extra money is a bargain.
Anyway, your old pc could possibly have bios issues with modern cards. Newer cards are UEFI instead of bios.
A low profile low wattage card is what you need, and gt 1030 low profile is supposed to work.
Your case has fit issues of all three dimensions for graphics cards.
You can consider selling what you have to buy a better used pc.
The old i5 gets close to a Core i3-7350K @ 4.20GHz 6625
I your pc, not sure whether you could find a low profile gtx 750
Some of the gt 1030's are low performance, some are good. The one you show looks like a proper GDDR5 ram version as OK.
If you can't get it to boot, it is about UEFI versus bios and may need to investigate a fix.