Imo if you want a desktop thats of good quality do it once and do it right. If you get a "low end gaming" computer, you are basically buying something that'll get along okay with most games now but will stuff on you later in the year and leave you playing on very low graphical settings or not at all.
I've put up with average computers for years, and I had to go budget when trying to buy a laptop which would play some of my games as well (I just managed to cope with an i3-370M and 512MB ATI Mobility HD card, even now it runs nicely but I need MOAR).
Compromise sucks when it comes to buying a computer. A budget of $800 will get you a lot less than waiting, saving a few hundred, and returning with a budget of $1100. Patience is hard but it pays off.
Now I'm building the ideal PC with all of the higher end parts I've wanted. Its not the most expensive or powerful gaming computer made, but its more power than I probably need for my gaming repertoire. It is the perfect machine for me, even down to brand name preference.
Its taken saving money, working a job for several months, and I'm also going to sell my laptop before it falls below resale potential so I don't cheapen out in any areas. And here in New Zealand, you end up paying a little more for components than the cost in US after converting the prices.
If you don't get what you really want, you are going to end up disappointed or looking to upgrade earlier than you might have wanted.
In my mind, building a computer is about finding the perfect case that reflects you design taste, and filling it with hardware that hits the nail on the head for your exact wants and needs. Every component should excite you from unboxing to installing and using. Any sense of disappointment or compromise shouldn't happen (within reason, if you want a $1500 graphics card you are being a bit excessive lol).
I've spent a lot of time with stuffty machines or a bad budget, and I know that is the reality for most. Not everyone can be as fortunate to be able to work up some money or find the funds. But if you can, don't be impatient.