You have an amazing opportunity here, so don't waste it by going straight to the newest games. I'd love to be able to forget the last 10 years of gaming and go through each popular release, from each year, gradually. You'll spoil the impact of the older ones if you go through the releases backwards (at least graphically if nothing else!). Gaming has gone downhill in recent years anyway, in my unpopular opinion, so you're only missing the odd gem.

If you have it in you, and you don't care much about online multiplayer, you could stay permanently a decade behind. Live your gaming life in 2007. Play anything before 20/05/07, but after that, play games as they "come out", based on their original release date. So many benefits to this idea! Super cheap hardware to run them effortlessly, super cheap games, permanently avoiding hype, and you still get to look forward to stuff. If you don't keep up to date on later advancements, these games would feel as fresh and exciting to you as they were to people when they first came out. 2007 was a great year in games by the way, Tomb Raider: Anniversary would be coming out in 2 weeks for you (a great and very traditional action adventure game, like what you're looking for, and often overlooked), and you have The Orange Box, The Witcher, Super Mario Galaxy, and Mass Effect to look forward to later in the year :P

But I have a feeling you're not very interested in a big gaming hobby otherwise you wouldn't have gone a decade without them... Sorry I'm just daydreaming here, and I know you asked for game recommendations. I can't think of anything offhand, but if you're interested in emulating the classics, people over at r/emulation should be able to help you a lot with that kind of thing. I would recommend getting an Xbox360/One controller for Windows, which is really easy to get working with pretty much anything, and the button layout works well for most emulation (not Nintendo).