Oh my, the expenses of life; I am just about surviving myself purposefully working for less money to focus on my project.
Well I hope your relationship with your child is good and all is well, so that when you advance in age your child will be motivated to give you the support.
So what do I think about the budget Alienware PCs? My first impression is that you would end up paying for name brand and a fancy case than you would for the performance.
The $400 PC you linked to is a definite no no. For the most part un-upgradable and in a small case; not very future proof. Bit of a media PC rather than a true gaming PC. It has an extremely low amount of RAM. Just 4GB (RAM not VRAM). This is not good enough; you'd need at least 8GB of RAM; I would not settle for less than 8GB for my grandma if she was still around.
The only PC I would consider using with less than 4GB with Windows 7 or above is a backup system, it would exist in a dark corner in order to simply store shit, I'd rather not consider to use it to run anything.
Props to Alienware for being able to market such a thing and call it a gaming PC. Unbelievable. It could never run any new AAA title on the market. As an avid YouTube user I can guarantee you'd be crashing the system after a few hours of watching YouTube videos, let along playing games.
Just as an example.
Sometimes DBPRO will use up 1GB to process a complex 3D level as it is loaded. With just 3GB left, a crash is likely to occur because Windows, Chrome, Firefox etc will eat up 3GB of RAM in no time.
If you want to treat yourself and want something to look good in the living room, then I'd definitely go ahead for one of them; preferably an Intel i5 or i7 with 8GB of RAM; 4GB of VRAM.
If this is all for quality gaming experience, general performance and suitability for games development; I'd invest in a more cost effective deal. Consider a laptop if you would not mind moving around with your system; low end laptops are actually just as good as low end desktop these days.
If you can learn build your own PC you will find that the end product will be a lot more cost effective and catered to you; however if you build it then you would have to spend quite a number of hours screwing things in, unpacking and installing Windows; not quite everyone's cup of tea. I did not build my current P.C. because I could not be bothered to plan it and build it at the time, but I regret my lazy attitude because I can tell the vendor installed the cheapest hardware he could find and it often crashes for no foreseeable reason. My last PC I will have not built myself.
If you have never built your own P.C. then I recommend you build at least one; you might find it is easier than you at first imagined. Judging by your budget, it seems like a self made brand new system would be a good investment.
Otherwise pick something with at least the following:
8GB RAM (Very important for running games, lots of apps. If you use lots of web browsing tabs and watch YouTube videos)
Intel i5 or above (if spending more than $400)
4GB VRAM DD5 GeForce or above (Shader model 3 for DBPRO, Shader model 5 for most popular video games)
1TB total harddrive space. (If as low as 500 GB, make sure it is SOLID STATE - Very fast, very reliable)
Windows 10, 8.1 or 7. Not 8.0. XP is lovely but too old now.
Stick to quality name brand hardware: Intel, Dell, NVidia, HP, Lenvono, Samsung, Corsair, Mushkin, Kingston, Crucial, Asus (probably in that order)
Personally I'd skip Alienware; they look cool but meh; its mostly about what's inside that counts.
As for Windows 10, it is good, although I prefer using Windows 7 and 8.1. Get any version from 7 with the exclusion of 8.0.
As a disclaimer this opinion based on personal experiences over the past 15 years. I've had bad experiences and have been told of bad experiences of hardware from the likes of MSi and Acer, however other people may have good experiences with them and bad experiences with the brands I recommended; generally the brands I mentioned do well.. If anyone had a bad experience with any of the companies I recommened please indicate.