There have been lots of good suggestions here. But what it comes down to is just the question of what you can afford and what you really want. What stuff do you already have?
There are two critical components you need that are not easy to upgrade at a low cost. That would be the motherboard and the video graphics adapter. But to get yourself started, you might opt for a good quality motherboard was just the integrated graphics chip. That would get you up and going, and you can get a better graphics card later.
Same idea with the CPU and the memory. Just yet and you can afford now and upgrade later. It's the motherboard that's going to be a hard choice. You need to get the best possible motherboard you can for the price. Do you have an old power supply that's working good? It probably will work well until you put in more memory and a better graphics card. So that would be another area where you could skim for now and upgrade later.
As for the case, what you really want? A really good-looking case? Or computer that performs well? The neatest, coolest, wild eye-catching case you can get will not do a thing to the performance of the computer. The case does everything it does even when a computer is off. So unless the appearance is important to you, don't think about the case.
Now if you don't have much in the way of parts on hand, think about this idea. Try to shop around and see if you can find a good used computer from a vendor you can trust. And I don't mean just on eBay. There are refurbished computers available through some of the top vendors and these come with limited warranties. These refurbished computers give you the best possible performance and price ratio you can expect. Some of the refurbished computers available are very hard to expand or build on, but check the specs out very carefully and you might find one that would fit your needs.
Forgot to mention. The good refurbished PCs come with a OEM load of Windows that is OK with Microsoft. That saves you some money.
Example: HP Pavilion p6240f Desktop PC - NO monitor, just inside your price range. Intel Core 2 Quad 2.5GHz Processor / 8GB RAM / 750GB Hard Drive / DVD±R/RW / Intel GMA X4500 / 802.11N / DVI-D / Windows 7 Home Premium 64-bit.
