I never had a powerful gaming PC before; a decent laptop but not a really powerful desktop PC.  I'm wondering if someone could help me out here.

I see a few places that look tempting to buy from, but I want some advice from some local experts. 

NOTE:  There are two schools of thought I'm going for, and aside of power I'm looking for good heat reduction as well:

1. A PC that is around $500 ($530 at most) with the best specs that you think you could find if you were buying it.

An awesome gaming rig around $500 would be my first choice, but..

2. I'm willing to go to $650 or at the VERY HIGHEST $700, but only if it completely blows anything around $500 away;  and I mean significantly.  Not mildly better, I mean top of the line and could last 5-10 years able to play anything at max setting.  I don't know if that's possible, but well here we are.

ummmm..

At what your willing to spend on, it looks like your trying to get the best performance out of every dollar but that isn't quite possible until you can build it yourself ...

OP, are you willing to do some tinkering around in order to get the best performance per price ?

Oh and maxing out every game in 5 years is impossible for just $700 today so you might have to spend more ...

Ok, nevermind then.  :P  A great gaming rig between $500 to $600.  Something you think you would buy.

A GPU that will play anything at max settings (1080p) for 5 to 10 years will be most of your budget by itself. 

A system with an i5 and a gtx 970  will set you back around 550 just for those 2 components, unless you buy used gear. 

Unfortunately it is pretty expensive if you really want a decent gaming pc, but you would be surprised how little difference there is between max and medium settings in most games.

For the most part, yeah.  What about bundles though?  Do you think you could find or build  a better and more affordable PC than the bundles provided out there?

Bundles ? 

Do you mean "pre-built" PCs ? It's pretty easy and it gets even easier when your looking for used parts at eBay too ...

Yeah, the issues I have with building a PC have to do with compatibility and balance (one-sided power on either the processing speed or graphics capability).  It's why I don't entirely trust myself to go looking for parts.  There could be hardware or software conflicts and so on and I don't want to spend any money until I'm entirely certain the balance won't be thrown off and everything will work together well as one cohesive unit.

for the price range youre looking at, you may well build a decent rig that can play current games, but it wont last very long before games are needing to be dropped further and further in quality to continue to run well.

I would strongly suggest a minimum target of $800-$1000 if you want the rig to last you a decent time.

$500-700 is considered budget level PC gaming.

No one builds a gaming PC with anything approaching a 10 year life expectancy, even for actual top of the line systems that run in excess of several thousand dollars.

This is very realistically what a $700 budget buys for a build it yourself gaming PC:

http://www.tomshardware.com/reviews/build-budget-gaming-pc,4065.html

Current Budget Gaming PC Components
CPU Intel Core i3-4150 (Haswell) $120
CPU Cooler Intel Boxed Heat Sink and Fan $0
Motherboard ASRock H81M-HDS, LGA 1150, Intel H81 Express $57
RAM G.Skill Ripjaws 8GB (2 x 4GB) DDR3 1600 F3-12800CL9D-8GBXL $64
Graphics Sapphire Dual-X Radeon R9 280 100373L $180
Hard Drive Western Digital WD Blue WD10EZEX 1TB $55
Power EVGA 100-W1-500-KR 500W $43
Performance Platform Cost $519
Storage Drive None $0
Case NZXT Source 210 Elite Black $50
Optical Asus DRW-24B1ST/BLK SATA 24x DVD Burner $20
Total Hardware Cost
$589
OS Windows 8.1 X64 OEM $100
Complete System Price
$689

As anyone familiar with PC components will recognize (anyone familiar will already have a good idea of what $700 in hardware will buy anyway) this is a competent but modest 1920x1080 gaming PC.

I suggest reading builder articles from Tomshardware.com to better educate yourself on what various budgets will currently buy and the tested performance numbers said builds will yield.