I decided this time around to just purchase a retail pc instead of upgrading my old hand built pc. Not the best idea but it's served its purpose so FAR. I was just wondering if I could upgrade my graphics card on this machine or not.

http://h10025.www1.hp.com/ewfrf/wc/document?cc=us&lc=en&dlc=en&docname=c03154290#N1272

I know the psu is a bit on the low side but there must be something out there better than my hd 7450.
It's also a pretty small case so that'll probably come into play as well.

Thanks for taking the time to read this You're going to be quite limited in what you can upgrade to, not only because the PSU is only 300W and your CPU is quite POWER hungry, but because it lacks any PCI-E power connectors.  The card you have is basically a rebranded 6450, which as you are aware isn't great for gaming.  I'd be hesitant to recommend a new card, because your 7450 has a TDP of 18W, any card that will give you a measurable increase in performance is ~70W or more, which is a fair difference.Well I could tear out my 600 watt psu from my old pc and use that. Would that help out things?It sure would, if that PSU is a good one.  What make and model is it?corsair gs600 It's pretty new so it should be fine. Oh I didn't notice that it was missing a pci-e power cord I suppose that does limit my options for anything too powerful. Anything will probably be better than my 7450 though.
The GS600 would be fine then.  There's really no sensible upgrade option with the standard PSU, you're limited to things like the 6670 and some low power versions of the GTS 650 if I remember rightly, which are overpriced for their performance.
I'd recommend the HD7770 as a decent mid/lower end upgrade, the 7790 if you want to spend a little more.  The 7850 or 7870 are still decent choices too.  On the Nvidia side, consider the GTX 660Ti, GTX 660, and GTX650Ti Boost.Well now the issue becomes what card can fit in my case. I have roughly 6 3/4 to 7" of space for the card. All the 7790s I've looked out have been too long to properly fit. I have however found a 7770 that will fit but would it be enough of an upgrade to warrant the 150 dollar purchase?
It's pretty much the best you can do if you're limited size-wise.  The 7770 is a capable card as long as you're not expecting the earth.Alright one last question and I should be good. I've found 3 cards that are short enough to fit in my case.

http://www.newegg.com/Product/Product.aspx?Item=N82E16814103233 - Diamond
http://www.newegg.com/Product/Product.aspx?Item=N82E16814131477 - PowerCooler
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150666 - XFX

I haven't used Diamond or Powercooler before but which brand would you recommend?
The XFX appears to have the wrong description for some reason, but the part number and price seem right.  Probably just a typo, someone copying and pasting the wrong description.

The XFX has a lifetime warranty, the Diamond has a 5 year (wow, when did they change that?) and the Powercolor a 2 year.
I've not had to RMA anything to any of those brands, and haven't owned a card by them.  When I was building day in/day out, we used a lot of XFX cards, had a few problems but nothing major.  We didn't use Diamond at all, they're not big over here, and we only used a few Powercolor because again they're not that common and if I remember correctly they're part of another company whose cards we may have used instead.

I would say it's pretty much a wash, if the lifetime warranty appeals grab the XFX, the Powercolor is cheapest and if the MIR works out it'll only be $80 which is pretty good.  The cooler on the Diamond LOOKS a bit DODGY, but to be fair they're all non reference and won't cool as well as a standard card so again probably a wash.I'll probably end up going with the XFX one because of the warranty.

Thanks for all the helpThat would probably be my gut feeling too.  You're welcome!