That is not true, the $180 mobos are for gamers. There are plenty of good Intel boards for i3-i5 procs in teh $50-$80 range. I personally like this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130588 Sure, it will never SLI, and overclocking is out of the question, but it will still be able to game decently, and do everything else.
My personal suggestion for what you want to do is get the cheapest mobo with quality parts (solid capacitors) and a UEFI bios if possible (lower boot time, easier to use, generally more features, and better win8 compatibility).
You will need 4-8GB of system memory, at whatever the stock speed is for your motherboard. And don't be afraid of value ram. Half the time it is the same thing as the good stuff but without the heat spreader, and if you are not OCing then it is fine.
Get an i5 quad core processor with at least 3GHz behind it, but it does not need to be anything special. Most CPUs are not the bottle neck of the system these days. It is generally the HDD, RAM, and GPU that could be faster.
Splurge on a small 60+GB SSD for your system drive. OCZ solid3 recently was 64GB for $80, more than enough space for the OS, a few browsers, an office suite, and the occasional game. I bought one for my wife's rig, and I will never go back. Sadly I need a 120+GB drive to hold my software that I would want to open faster, but then again this is a work machine for video/audio editing and gaming, not a simple desktop, and the prices will come down by the time I upgrade next year.
Buy a minimum 1TB HDD for files, large programs, and system backups, or as a system drive if you opt out of the SSD
Win7 home premium 64bit for the OS unless you are willing to try linux which has some compelling distros out there. Personally have toyed with Fedora and Ubuntu, and have enjoyed both except they wont run some of the software I use (yet). Windows is $100 which will eat a large chunk of your hardware budget if you have to buy a copy. Go pro if you ever plan on doing a real network in the house.
Buy the cheapest case without a power supply you can find that will suit your needs. Really, who looks at their computer? I splurged a bit on mine, but as my last $40 case lasted 10 years and 6 rigs (3 rigs were replacements due to bad power instead of upgrades, I only upgrade every 4-5 years), my bet is that this will last another 10. Sure you don't want a white crappy looking thing, but there are a ton of sub $40 cases that have simple elegant designs and will work for most things.
Find a quality power supply that is appropriate for your system (likely 500W or less, but it depends on the specifics of your CPU+GPU). Built-in power supplies suck, as do most cheap PSs, computers become expensive when you have to replace parts due to bad power as I have lost 3 that way. But a good PS will last for several PCs. My PS is on it's 3rd rig, and I think it will handle my next system just fine until I start SLI or xFire, and it is a simple 450W. Do not overblow your wattage on the PS as you will always be paying for unused power.
Save the GPU for later, and use the onboard graphics until you can afford a nice one. This will likely be the most expensive part of the system, or at least equal to the CPU, and will be the main limiting factor of what your rig can accomplish. With your resolutions you do not need a ton of vRAM, just aim for horsepower and you will be good. My suggestion would be the highest end of a previous series, or a upper-midrange card of a current series. When push comes to shove look for the card that supports the latest DX and OpenGL standards. Also, remember that AMD and nVidia are refreshing their lines in Q1 of 2012 (AMD may be sooner), so onboard graphics may be 'good enough' until March when the new stuff comes out. All of the new cards are promising lower power consumption, which generally means less noise and heat, which means a smaller and cheaper case, and a smaller power supply! Save money all around
Remember that Microcenter and Fry's often have great sales, even if their normal prices suck. If you live near one you can save a ton of money on processors, mobos, and HDDs. Also, Ink is right saying you can get more bang for your buck with AMD in this price range. You may get more performance out of the intel rig for the same price, but you are sacrificing a richer feature set and expand-ability with a cheap mobo.
General budget for Intel system:
Windows =100
Case <40
PS <50
Mobo ~70
i5 2400 =150 (at a microcenter, $190 at newegg)
RAM ~25 4GB (2X2 value ram)
SSD <90
HDD ~55
Total: <580, without GPU
Obviously, if you have a case/PS/OS you can reuse then it is much cheaper and you could afford a nice GPU to complete the set. The SSD is a splurge, but I highly recommend it, and would only give it up if you cannot afford to buy the GPU later.
You can do all of your daily work, multimedia, and light gaming on the i5's HD2000 (which was your requirement, and HD2000 has HDMI out on most mobos), and then go nuts with a good GPU when you can afford it. This setup will game very well without bottle necking a mid-high range GPU. I recommend a 560ti for $260 (or AMD equivalent) as a separate purchase from the main system build. But like I said, this will not choke a 570 if you want to splurge, and could take a 580 (but may bottle neck a little), but 590 is out of the question. The only thing missing from the high end builds is overclocking, SSD cashing, USB 3, RAID, high end audio, extra 2 RAM slots, and some other features. In spite of the features missing, the speed of the buses and interconnects will still be there, and that is what counts in a budget machine.