Mom needs computer buying advice lol

I'm trying to buy a PC on a VERY limited budget and this one seems good on ebay-the guy built it himself nearly 4 years ago and seems knowledgeable when I asked a few questions-I just need advice on if this is decent enough for mostly my kids. For $220 it seems ok. They want to play Minecraft w/mods installed, Lego worlds, and my older one possibly games like assassin's creed 4 black flag, etc. Advide from people who know what they're talking about is much appreciated! Here's the info from the ad:
Custom built desktop PC with i5 650 CPU, 8G RAM, 250G HD, and AMD RADEON HD 7570 GPU. Has a high quality Seasonic 300 watt PSU. Monitor, keyboard, mouse are not included. Power cable and VGA adapter for the graphics card are included. The i5 650 is a fast dual core processor with hyperthreading, so it displays 4 threads in Task Manager. It is comparable to some of the current generation Core i3 CPUs. This CPU is over clocked to 3.575 ghz and turbos up to 3.718. This is a conservative overclock which runs very cool and stable. This has an H55 LGA 1156 motherboard which has 4 slots for RAM. I believe these motherboards can have up to 16GB RAM. Right now it has 4x2GB 1333MHz DDR3 Kingston RAM sticks. So all the slots are full right now.

The HD 7570 GPU is an OEM entry level gaming card with 1 gig DDR3 VRAM. It uses an OEM driver which is already installed and a copy is also on the desktop. I would recommend keeping the OEM driver as-is and not using a newer AMD driver.

Jammie 13.07.2015

First laptops are never a good purchase for gaming as they will for sure lag and not be as fast as you want them to be unless you plan on buying a laptop of course made for gaming but those run easily into the thousands of dollars and to get one with minimal lag and good specs your looking at around $2,000 for the basics of a Alienware or alike laptop.

Desktops run much cheaper as they do not need to be portable also so that knocks price down a whole lot and also they are capable of lag free gaming for much less as the spocs generally are higher in a machine that is not built to be portable and small as can possibly be as well as light weight. Your still looking around 4-800 for anything truly good I suggest never buying used computers especially without being able to run it before getting it that in it self would be a major worry as your stuck with it once you get it and you never know what type of problems can arise shortly after getting it. The best bet always with computers in my years of experience is never buy used always buy new and buying what you pay for is what you will get when speaking about computers! Hope this helped!

Tweaked 13.07.2015

I would probably pass. That processor is a Generation 1 i5 and the newer i5 chips have definite performance advantages. The power supply is a little under powered and unless you are doing serious gaming there's no reason to overclock that computer. I would wait and look for something with more modern specs, it may cost a little more but the performance and reliability will probably be better. You might want too look at refurbished or off-lease computers to get something newer at an inexpensive price.

Herman_Miller 13.07.2015