Ask those questions to 10 people here and you're gonna get 10 different answers.
1) "So first, what are the critical computer features needed for games now and let's say what you anticipate will occur in the next 4-6 years - minimums and recommended and assuming it's a laptop/touchscreen where adding a separate monitor is out of the question (I have my reasons for that)?"
This is called 'future-proofing' the machine, and generally isn't as drastic as you may think, as often a computer can last years upon years with gaming, the less you care about fancy graphics the more it will last Now, you're an MVP, so my apologies if I seem like I'm treating you like a newbie here, I don't mean to insult your intelligence but I'm going to tell you the why of some things.
There are three things you want to consider with gaming, the first is what kind of gaming do you want to do? Mobile gaming (laptops NOT tablets) or desktop gaming? The second is that you want to consider that not all games are created equal and some will perform a lot differently than others, thus there's never a true 'perfect' minimum requirement and the third is if you wish to save yourself the hassle and just play console (Xbox and Playstation etc).
Now to answer your question: Minimum requirements and keeping in mind future-proofing assuming we're at 2012 standards are as thus:
4 GBs of DDR3 memory
250 GBs of storage
512 GB DirectX 11 video card
650 watt 80+ Bronze certified PSU
Going anything less than this wouldn't be a wise move, sure you can play games with less, but this is a very very modest minimum that any budget can meet.
Recommended specs for the same situation would be not much more:
6 GBs DDR3 memory,
600 GBs 7,200 RPM storage
1 GB Directx 11 video card
750 watt 80+ Silver certified PSU
2) Next, what would be your top 3 picks for a beginner and, if it differs, your top 3 picks overall.
I assume you mean which games? This one's pretty hard, especially considering you've never done any real gaming. My top 5 are not beginner-friendly, and games are rarely rated on their barrier-to-entry (what we call the difficulty to start and learn the game).
The types you generally want to start with are 'casual' games. I'd recommend a lot of indie games, like Limbo, Brine, Legend of Grimrock. When you're ready to move on to a more challenging game action-wise games, try Half-Life 2, it's a monument of gaming success, a literal beacon of greatness, it's the industry's Pulp Fiction or Citizen Kane. If you're ready to move on to even harder games, consider a role-playing game, try The Elder Scrolls V: Skyrim.
We can certainly take this to PMs or Skype etc if you wish to discuss this further!