Unfortunately computers are a lot like cars, everyone has their own individual preferences, likes and dislikes and as such everyone will have different recommendations.

Yes, it is true you can generally save a small amount of money shopping online and assembling the pieces yourself, however in the long run this savings can be easily offset by something as simple as memory incompatiblity or a hardware failure of some sort.

It's true that you can still get these parts replaced under the 1 year manufacturers warranty, however if you buy the parts seperately that means you have to pull the part out, ship it to the online retailer or wholesaler you bought it from, have them ship you a replacement and then install it yourself.  Also when purchased seperately processors are not warranted against heat damage or poor installation, so if the company your dealing with says the damage was caused by overheating your in a world of hurt, they won't replace the processor for you. 

For the more technically oriented the small savings you get for shopping online might make that attractive, however for the average user it is generally a lot easier and a lot less expensive in the long run to have a store front that you can simply drive too, drop the system off and have them deal with all of that should any problems arise.

It is true that if you price the components individually you will be able to get much better deals online than you can at a storefront, however if you buy a pre-built bundled system the prices are going to be hard to beat, particularly if you have to pay someone else to assemble the hardware.  Best Buy can generally sell systems cheaper than most other shops can assemble them because of their vast purchasing power, they get much better prices on systems than most other retailers/wholesalers.

As for Emachines or HP's, I've worked extensively with both, as well as Dell's and of course just about every type of clone archeticture known to man, I've been in the IT industry for over 20 years now.  In truth I've found very little difference in the systems themselves other than upgradeability, and considering your budget, the type of system you're looking for I still say your best bet will most likely be to buy a machine bundle rather than individual components, merely from the warranty and return aspect.  I've installed literally thousands of Emachines over the last several years, I have yet to have a major problem with any of them.  Truth be told their track record in this regard is slightly better than HP or Dell, though HP machines are a bit "prettier" to look at.

Just my two cents worth, naturally opinions will vary but that is my recommendation.