Looking for a new graphics card

Hm. you do make a valid point.
and I second the option of the HD7870. I helped a friend install one of those into his rig and it's a powerful card to say the least.

Any cheaper card options?

Absolutely. but remember, the cheaper, the lower the performance.
The HD7850, which I listed before, can be found for around $220-240
then there's also the GTX 560, which is a step below the HD7850. the 560 is around $180-200
Below that, there's the HD6870, which can be found for about $160-170
then if you really must go cheaper, there's the HD7770, which you can find for around $120-140.
that's the lowest I would go though, if you want to do any gaming.

Here's a hierarchy of graphics cards so you can do a bit of perusing (scroll down a bit)

Okay, so say I decide the gtx560 and the antec cooler... is this a good choice? and where should I buy them from?

http://www.newegg.com/Product/Product.aspx?Item=N82E16814130661 <<< any thoughts on this particular buy?

Antec cooler? what do you mean by that?
also, the 560 is an OK choice for moderate gaming on medium/high settings.
I guess that's a good choice. and where you buy from depends on where you live.
for USA and canada, www.newegg.com or www.tigerdirect.com
for Australia, www.pccasegear.com or www.msy.com.au or www.umart.com.au
for the UK, www.scan.co.uk

it's OK. EVGA make nice cards. it has 2 DVI outputs so make sure your monitor supports DVI.

Sorry, I meant the Antec power supply:
Newegg.com - Antec NEO ECO 620C 620W Continuous Power ATX12V v2.3 / EPS12V 80 PLUS Certified Active PFC Power Supply

and the card:
Newegg.com - EVGA SuperClocked 01G-P3-1461-KR GeForce GTX 560 (Fermi) 1GB 256-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card

Would this be a good combo for the $$$? and what kind of issues should I look into before buying? and yes, my monitor does support DVI.

Looks fine to me. it's a good step up from your current performance level.
although if you can afford it, why not go for the 7850? it's much faster than the 560.
here's the Sapphire HD7850, which is $189 after MIR.
it would easily outperform the 560 in gaming. plus, it has a nice cooler so you can expect quieter, colder performance.

Hmmm yes, I do like this suggestion.. But as to my other questions, what kinds of problems could go wrong? and what should I be looking for as far as reliability?

And whats the significant difference between a regular gtx560 and a gtx560 TI?

To answer your first question, nothing should go wrong. the PSU and GPU are compatible, and as long as you don't screw up the actual installation (which is difficult to mess up), you'll be fine.
in terms of reliability, Antec is a great brand if you want reliability, and for the graphics cards, EVGA and Sapphire make great cards. The only thing that could go wrong is if you get a DOA (dead on arrival) card. even then, that only happens maybe 2% of the time.
In terms of longevity and future-proofing, then the 7850 is the way to go, since it's a newer architecture than the 560.

to answer your second question, there is a difference between the 560 and 560Ti, but it's not incredibly significant. I won't go into the technical details, but basically the Ti version is just more powerful than the non-Ti version, simple as that.
even then, the 7850 is still faster than the 560Ti.

Yeah I'd really recommend the 7850 over the 560 as well, you also have twice the VRAM so will last you a lot longer. 1GB of VRAM is not really acceptable any more for games nowadays.

Alright, great! I will most likely order these by today or tommorow. ( the 7850 and Antec power supply). On a side note though; Will I be missing any features from NVidia that radeon doesnt have?

Main thing you'll be missing is PhysX, here's a list of games which use it. Be aware that it's quite taxing in terms of GPU performance so if you do like the PhysX effects then you should go for a 660Ti and above.

Well. that's a long story.
in terms of features, it's apples and oranges. both AMD and Nvidia cards have fancy pants features which make stuff look shiny.
Ok, that's a huge generalisation, here's a quick read which may give you a heads up.

Ok, so I have chosen this card:
Newegg.com - SAPPHIRE 100355L Radeon HD 7850 2GB 256-bit GDDR5 PCI Express 3.0 x16 HDCP Ready Video Card

and this power supply:
Newegg.com - Antec NEO ECO 620C 620W Continuous Power ATX12V v2.3 / EPS12V 80 PLUS Certified Active PFC Power Supply

So, will these installations correctly fit and work fine in my HP Pavillion HPE h8-1110?

The power supply in my pc has a fan that faces outwards toward the back, not down inside the pc as in:

Newegg.com - Antec NEO ECO 620C 620W Continuous Power ATX12V v2.3 / EPS12V 80 PLUS Certified Active PFC Power Supply

It has vent holes for a fan to be facing outwards in the back of my pc

Any more comments?

You'll be fine.
just make sure you watch a TON of instructional videos so that there will be no margin for error.
when you mount the PSU, make sure the fan is facing toward the inside of the case, so that it's not suffocated against the panel.