MW2 is a game born in an era of innovation from Infinity Ward that you don't see much in their later games, it's also more simplistic and bare-bones which allows you just to enjoy the moments without constant chaos that forces you to press respawn every 10 seconds. Depending on his age he might either love this title in the CoD series or turn his nose up at it, as far as most fans are concerned, after this game is when CoD started to go down hill chasing its own tail.

I'd say got for it, but if he likes the chaos and over-the-top action that the modern CoD's bring to the table, maybe go for one of the new Black Ops titles or MW3. In terms of graphics, they all pretty much look the same.

I'd say that it's a bit of a gamble as to whether he'll like it, especially if he seems to be playing more of AW. AW came out 6 years after MW2, so it is a lot better graphics-wise. Additionally, AW introduced new movement mechanics, making the game much more fast paced in comparison to previous CODs, hence making MW2 seem somewhat slow in comparison. This game is worth a shot at just over £4, but if he gravitates towards AW over BO, you may want to get him either Black Ops 2 or Black Ops 3 instead

That sounds like a good choice imo being the most recent CoD release (although obviously more than 5x the price of the deal in this post). Only thing to be aware of is that there have been some issues reported with the PC version so it might be worth double checking if they've been resolved/ if the game works with your son's PC specification.

If you're talking about MW2, you'll be absolutely fine, the game is well optimised and has low requirements:

Processor: Intel Pentium 4 3.2 GHz or AMD Athlon 64 3200+ processor or better supported
Memory: 1 GB RAM
Graphics: 256 MB NVIDIA GeForce 6600GT or better or ATI Radeon 1600XT or better

If you mean Black Ops 3, minimum listed on Steam is:

Processor: Intel® Core™ i3-530 @ 2.93 GHz / AMD Phenom™ II X4 810 @ 2.60 GHz
Memory: 6 GB RAM
Graphics: NVIDIA® GeForce® GTX 470 @ 1GB / ATI® Radeon™ HD 6970 @ 1GB

I know they've patched the issues with i5 processors, so you should be sorted there. Other than that, looks as though you'd be able to run it, just probably not on any high settings.