$800 - $900 budget gaming PC build

Do you have an Intel/AMD preference? Any other preferences beside budget?

Okay, I threw together an idea for a budget gaming rig, consider this more as a starting place, we can customize as you want.
First off I want to say that I am assuming that you already have peripherals such as mice, keyboard and mouse. I am also assuming that your rig will be be connected by ethernet and if not, I can help you look for a good network card, but for gaming it is highly recommeneded for ethernet.

So, when it comes to building a gaming pc (in my opion at the very least), the video card is the most important part. After that, storage, cooling and cpu. Then the rest.

Here is the list I came up, with explanations.

Video card: XFX Double D FX-787A-CDFC Radeon HD 7870 GHz Edition
This is a really good video card for the money, plus, comes with some cool games. This card will be able to take on those games at high quality settings without a problem.

CPU: Intel Core i5-3350P
I found this under TomsHardware Best Gaming CPUs: $110 To $200 review. The P means that integrated graphics is disabled, but that isn't really important because you will be using a graphics card. It also has less power usage. If you do want to use integrated graphics, or if you have interest in overclocking let me know and we can arrange that.
The reasons I chose Intel over AMD are 1) I have never owned an AMD processor, the two laptops I own and my gaming rig all have Intel and I have never had a problem. 2)Intel CPUs process more instructions per cycle and AMD CPUs do and as a general rule, the top gaming CPUs have been Intel.
That being said, which CPU you choose is not to important so long as it can be fast enough to not bottleneck the GPU.
If you want to try and save a few more bucks, we can look into some AMD alternatives, but this CPU does come with really good recommendations and reviews in terms of gaming.

Storage: WD Black 1 TB 1TB should be enough storage for you and this is a pretty good drive for gaming enthusiasts. If you think its a little pricey and loading speeds arent as important to you, we can find you a good WD Blue option or a Seagate Barracuda.

Motherboard: GIGABYTE GA-Z77-DS3H LGA 1155 Intel Z77 This motherboard is a little bit on the cheaper side, but budget is important and Gigabyte is a good brand. This should do the trick for you. Unless you have decided on overclocking, then this might not be the best option for you.

Memory: G.SKILL Ripjaws X Series 8GB (2 x 4GB) 8 GB should be enough for a gaming rig and if you want, we can always go more. I chose the 2x4GB because I personally prefer dual channel. I made sure that everything is capable of that. That being said, dual channel is usually more noticeable when you are multi tasking, therefore it might not be as important for the actual gaming part. If you aren't interested in dual channel and would like to save about $10 then you can get the one stick version here. Do note that the Timings and latencys are slower on the one stick, if that is important to you.

Case:When looking for cases, I wanted to make sure I kept it under $100. I have a certain love for cooler master cases so I picked the COOLER MASTER HAF 922 for you. That being said, if you want to spend less on the case I suggest reading here. Tomshardware does a review on four sub $100 gaming cases that might interest you.

PSU: For power you will need around 450W. I looked for a 500W PSU to stay on the safe side. If you have plans on upgrading it might be better to invest now in a better PSU rather then spend more money in the future to upgrade one. Brand-wise, you can't go wrong with a Corsair PSU. Cooler master also makes some great ones but they also have a few that are not as good. With that, I chose the CORSAIR CX500M 500W ATX12V. That has can take care off all your current needs.

CPU Cooler: This is sort of something I haven't focused on. Personally I find the stock intel CPU cooler to not be as good as others, but it should be able to handle what you want to do. While gaming, I would focus on the CPU temperatures and if you feel they are getting to high, you can always look into CPU coolers. CPU coolers are divided up by two categories, liquid cooling and air cooling. That comes down to personal preference that we can discuss in further detail if you want.

As for things like an optical drive, you can grab a cheap $20 at places such as frys for CDs. On my rig, the optical drive is the cheapest thing I have. What I do is I use daemon lite to copy the cd into my computer so that when I want to play the game I just virtually mount the cd. I find that to be much more efficient that switching out CDs.

Sorry it took me a while to get back to this post. I hope you find this information useful and if you have any questions or want to change a part feel free to post.