Graphics Card upgrade recommendation for HP Pavilion s5610f

[SpaceThunderV]

I'm getting a referb Lenovo Thinkcentere desktop with good specs for video editin' and win 7 pro 64bit, as I WILL NOT TOUCH WINDOWS SPYWARE 10 WITH A 9000 FT POLE! When it comes in the Lenovo and proves reliable, it will be my main unit to replace my peppy but kinda sluggish HP Pavilion s5610f Slimline Desktop. However, I still want to keep the HP around as its wayyyy better than my acer lappy which is on its last legs. I plan to put some things like a graphics card in the Pavilion, maybe fool around it with a bit since it wont matter what happens if I flick something up on it LOL.

HP's specs are:

H-Apricot-RS780L-uATX Motherboard

AMD Athlon II X2 250 Dual Core 3.0GHZ Processor

two DDR3 DIMM (240-pin) sockets with 8GBs of RAM (upgraded from a measly 3GBs LOL)

64bit Windows 7 Home Premium preinstalled (OEM)

ATI Radeon 3000 Integrated Graphics

640GB Hard Drive SATA 7200RPM

Is it possible to shove in a graphics card into it? I was told that it has to be low profile and its mobo only accepts PCI x1 or something and most I see are x16. My Google-Fu hasn't been of much help finding answers specific to my model though, as I see dope questions where some chap needs to upgrade his kid owned HP s5620, 8000, etc. with dinosaur processors and Raedon 2000 shit because he dropped Hot Coca all ovr his $20,000 gaming rig or something like that LOL

Please note: IM NOT A HARDCORE GAMER! Mainly, I'm looking for something that can boost video conversion for Freemake video converter and my video editing software (Sony Vegas pro 11), as a friend of mine told me some cards can assist with video rendering but he wont tell me which ones because he doesn't want competition. Speaking of him hes loaded in cash and got this kray kray gaming rig with all sorts of things AMD 8 cores, 5gb video card and its 1s rendering for a 2 hr movie and Doom running 60fps at 1080p its phucking awesome bro.

EDIT: I was also told I have to upgrade my PSU on the HP if I put a card in its PCI slot or the cpu will choke or something. I don't know the wattage of my PSU and nothing on Google says anything about a power supply swap if I put any video card in so plz help me i'l give you a Scooby Snack LOLOLOL