Most people will tell you to go with one of DFI's motherboards. That's because most of them are overclocking gurus and people who like to spend a LOT of money on really expensive and flashy hardware.
Honestly, I don't think it's necessary to go with DFI to get a quality motherboard that won't let you down. DFI motherboards, from the research that I've done, have proven to be unstable at stock speeds in some instances as well as difficult to get set up initially. There have been a number of people who have had issues with certain kinds of memory with a DFI board - Corsair comes to mind. They also tend to require a lot of higher-end hardware to truly perform effectively, and being that you're looking to spend $600 or so on the system then it's probably not the motherboard you're looking for.
But that's not to say that you have to totally eschew performance because you're on a budget. I'm actually in the process right now of building myself a new computer with a budget similar to yours, and I've narrowed my selections for an Athlon 64 motherboard down to two boads made by EPoX:
The EPoX 9NPA+ SLI (nForce 4 SLI) board or the EPoX 9NPA+ Ultra (nForce 4 Ultra) board.
While the EPoX boards don't have as massive the overclocking options as the DFI boards, every review I've seen on either of them has said that they're both extremely good at overclocking (probably one of the top contenders for overclocking).
They're very stable as well and have a lot of nice features that go with them. They both have Onboard LED indicators to show the power status CPU, AGP and DRAM as well as a post-port LED display to assist you with troubleshooting. And if you go with the SLI board, it comes with a temperature sensor (they call it a 'Thermo Stick') that you can use to monitor the temperature of something or other - always a nice bonus - as well as a little fan to cool your MOSFETs.
There are many more extra features that come with both motherboards, but you'd have to go to EPoX's web site to look at all of them. I'd rather not type them all out here, but needless to say I think that the EPoX feature set is impressive. I really haven't seen any negative reviews for either of those EPoX boards and I can see why.
As to which one would be best for you, well, it all depends on whether or not you want to save a little money now or plan ahead for the future. There's about a $30 price difference between the Ultra and SLI board.
If you're really looking to save some cash but still get a great motherboard with excellent overclocking options and features, then go with the Ultra board. If you want the ability to buy a graphics card now and then put another one in the motherboard for added performance later on when (if) you can afford it, then get the SLI board. The SLI board will probably overclock a bit better as well since it uses four-phase rather than three-phase power.
To hopefully give you an idea of what these boards are about, here are some reviews for both of them:
9NPA+ ULTRA
http://www.ocworkbench.com/2005/epox/ep-9npa+ultra/g1.htm
http://www.transmetazone.com/articleview.cfm?articleid=1747&page=12
http://www.xbitlabs.com/articles/mainboards/display/epox-9npa.html
http://www.pcper.com/article.php?aid=124&type=expert
9NPA+ SLI
http://www.ocworkbench.com/2005/epox/9npa+sli/g1.htm
http://www.tbreak.com/reviews/article.php?id=362
http://www.pcper.com/article.php?aid=138&type=expert
Hope that helps. Oh yeah, and...if you want to get something from the GeForce 6 series, go with a GeForce 6600 GT. They're offering a terrific rebate deal on a good brand of 6600 GT on MonarchComputer:
http://www.monarchcomputer.com/Merchant2/merchant.mv?Screen=PROD&Store_Code=M&Product_Code=190325
I'd prefer AMD processors and something from the GeForce 6 series. I have no clue what's a good mobo for the 64 bit processor, so I'll definatly need a recommendation for that. 
