So I want to be able to play current games on my computer but when I try, it is really bad. When I play bioshock infinite I have 10-15 fps when on the lowest graphics settings and no other programs running.
My question is should I change my cpu or gpu or what? and to what
price range is preferably below $250. Processor is Intel Core i3-3240 CPU 3.40 GHz. 7.87 GB usable RAM. 814 Gb of free hard drive space. I'm not quite sure what my gpu is since when I go under device manager, it just says Intel HD Graphics, but I remember reading somewhere that it is 2500.Sounds like you have a motherboard with integrated graphics.  If that's the case the the best bang for your upgrade dollar WOULD be athe best gpu you could afford.As strollin said, your biggest limitation is your video card so this could really do with being upgraded for gaming.   The only thing to really check with this is that your current power supply is capable of running a video card as if it isn't it may need to also be upgraded.

What make/model is your current power supply?  This is the big box inside the PC where the power plugs into, there will be a STICKER somewhere on that that gives the make/model.btw... we are all assuming this is a desktop computer that should EASILY take an upgrade... if this is a laptop your most likely stuck with the Intel HD 2500 integrated graphics. Also impressed that the Intel HD 2500 is able to get 10-15 fps on integrated.... I would have bet on it being much worse such as around 3-5 fps given the GPU demands of that game.  Yes it is a desktop pc. I'm pretty sure it is a DELL inspiron 3000 series. But again, don't know for sure if the gpu is actually 2500, I just think. Power information is attached.
 Edit: sorry the picture is upside down. Don't really know why.

[recovering disk space, attachment deleted by admin]Cool, in that case you have a 300w PSU.  This is pretty low for high end video cards although SOMETHING like an NVIDIA GeForce 750ti would be fine on it.  Alternatively, if you want to get a higher end video card than the 750ti, you would need to also upgrade your power supply, do not cheap out on this, make sure you get a good PSU from a reputable brand, not some generic brand one for $20!

It all comes down to how much you want to spend on the video card and potentially a power supply.Alright cool. ThanksIf you upgrade the GPU ( go to a dedicated card ) you have the issue of the Power supply, in that it will not be enough ( Probably no PCIe connectors or not enough ). If you do go that route, then there may be an issue of the CPU bottlenecking the GPU. To be honest there is no real modest budget fix.