Evening,
The problem with PCs is similar to camera bodies, and that is that they are eventually going to go to 0 value sometime. They are a depreciating asset. Here on the kitchen table, I am using a little HP netbook for a couple of hundred. Under powered with a small screen - absolutely, but I can take it with me to review images immediately (when I travel), and it works out pretty good. Note, I said review - not really post process. Down in my office, I have a Dell no name - pretty underpowered box from Costco that I picked up for $500. I did pop in a low end graphics card to help it along, and it does pretty well with Oloeno, LR4 and Bibble Pro 5. So, its not the fastest, but it does all right.
At work, I have a real small (form factor) Dell laptop because I just got tired of shlepping a large brick through the airports that weighs a ton. In my lab, I have the absolute fastest that Intel and AMD want to provide me for evaluation, along with a ton of servers paired with custom builds and network infrastructure, for special projects.
Now after having said all of that - on a budget, building your own system is really fun, but the bottom line is that Windows costs $175 bucks - that is a tax. Adding that on top of the hardware turns a $500 box in to a $700 box. The box makers get their Windows OEM for a lot less (on the order of $20), along with a lot of pretty cut rate parts in large quantities. Thus, the bottom line is that you can get a pretty powerful box, 4 cores, 8 GB along with 1T of storage out the door at $500 with Widowz. No graphics since it is built into the processor chip. An i3 or i5 has plenty of CPU power to brute force LR4. You can get a cheap $50 graphics card to possibly help with post processing, but the money would probably be better spent on an IPS monitor.
The laptop is yet another good idea. Asus and Toshiba are good brands. Building your own Laptop can be a real chore. We have done it at work for various reasons - special projects. prototypes, etc. You run into the same problems with laptops in terms of cost - it spirals up pretty quickly.
Where custom builds really shine is with Linux, since the distributions remove the Windoz tax. When you couple that with tuning your specific processing needs you can do very well. Trying to bring a custom build in at a $500 price point is pretty difficult, when you go down to Costco or wherever and start comparing raw functionality on cost.
Going up to something like a $700 - $800 cost, does give you sufficient margin to start to customize on a very powerful system. My son during Christmas - coupled with some really excellent sales, nailed an extremely nice system. Also, being a student, he was able to download windows for free (Microsoft essentially gives away software to students for nothing to hook them on their products when they go out to work). Thus, there is no OS tax.