Yes, I think if you don't install a Disc drives, and other un-needed parts which you don't need like a webcam, microphone, etc, building a Gaming PC could be cheaper than building a Gaming PC with a disc drive, multiple video cards, webcam, microphone, a fancy case, and other un-needed parts, or even cheaper than a lowend computer you buy from a retail store.
There are videos on YouTube to help gamers build gaming PCs for around $350 and up to play many games on High video quality settings, and more intensive games on Medium settings.
Example video of an Intel Gaming PC built with only $350.
A disc drive is the simplest way to install the OS. I think you can get one for a few dollars at a used computer store, or from a friend or a family member's old computer.
I think you can use a USB flash drive to install Ubuntu Linux and Linux Mint. USB thumb drives are pretty easy to get for free since I remember a Beer company here was giving away free USB thumb drive when you bought a pack of beer, and some people maybe willing to lend you their empty USB flash drive for a few hours to use it to install Linux.
Using a traditional mechanical hard drive over a Solid State Drive will also make a PC cost less since a 500GB drive only cost $50, and 500GB is enough storage for many people who only play a few games at a time, and uninstall games they no longer play.
I would get a disc drive anyway. They are very cheap $10-$20 and are useful sometimes. If your on a budget check out newegg for a budget case. Also, 500 GB is more than enough if you just plan on playing games. I have a laptop with only 320 GB of storage and I haven't run out of space yet and I play 2 mmorpgs(large installs). SSD are good if you have the extra money to toss about but if you're on a budget just wait until they drop further in price in a year or two.
Also, I wouldn't go less than 4GB of ram. And another thing don't cheap out on the video card or power supply. Some people overlook how important a power supply is and always overate the total wattage you need to power all your components. Some good brands are corsair and antec... avoid cheap/noname brands like the plague. You might already know all this however but if you don't or someone else doesn't I feel like I've given them some of the basics.
I think there are some computer cases which come with good power supplies in the 400W category, and made by better power supply makers like Cooler Master and Thermal Right which also makes cases.
3GB of RAM is good enough if you use a 32Bit Operating System like Windows XP-8.1 32bit because you don't want to buy Windows again, and use the 32Bit version which came with your old Windows PC. I read that a 32Bit OS can only use 4GB of RAM, but if you have a video card with 1GB of RAM, you can only use 3GB of RAM because of the 4GB limit. Also, for 32Bit Operating systems, I read on a forum that each program can only use a maximum of 2GB of RAM. If you turn off a lot of the features which you don't use in Windows like the animations, special effects, and use a light weight antivirus like Vipre Antivirus or NOD32, the RAM usage in Windows can be less than 1GB. I gotten Windows 8 down to 454MB of RAM usage by turning off stuff I never use in Windows.
I think with cheaper video cards like the Geforce GT 650 which you can get for $90-100 if you look around are pretty good for playing most games.
Although, if you can deal with lower quality levels for graphics, or playing older games, sometimes older video cards like the Nvidia Geforce 550, or cheaper cards like the Geforce 620 can be good enough for gaming. I use a Nvidia Geforce 620 which I got for $60, and it can play many older and less intensive games on my older computer.
Using the standard Air fan cooling can save a little bit of money as well since water cooling is expensive, and better fans and heatsinks for fans can cost more. The standard cooling which comes with a case, CPU, video card, and powersupply fans should be good enough for most computers which aren't overclocked.
I wouldn't go lower than 500W or 600W on the power supply if you plan on gaming. I have a computer just for checking email/ internet/ youtube and it has a 400W power supply. I've even heard you should go 1.5x your rated total wattage. So for example if your total componant output is 300W you should get a 450W power supply minimum. This leaves room for upgrades for one thing.
And don't get built in power supplies unless you are fine with mediocre quality and possible loud fans.
As for the 32 bit OS most people should really think of upgrading to 64 bit OS since you get more out of your ram even if you have just 4GB which is probably the low mark for modern games. And yes shared memory will take effect if you put a video card into a 32 bit OS powered computer. The computer I'm on now has a 256mb graphics card(not my gaming computer) but I only have 3.25 gb available out of 4.00gb. If I was on a 64 bit OS I would have all 4GB available I think.
But you seem to know more than I do about graphics card so I have nothing to say about that lol.
