Amiga:
Civilization - there's no game in this world (imho) that makes time runs faster. You can start playing (for example) at 20h, and you play 2-3 hours, and then you realize it's not 2-3 hours, but it's 5-6AM and the dawn is approaching.
To get into it easily, I suggest looking at some youtube gameplay videos.
K240 - amazing realtime strategy, very fun for playing. Easy to learn.
Frontier - Yeah, that's a good choice. It's not really hard to get into. I also suggest watching some youtube gameplay videos, and you're good to go... it's really easy, once you get into it.
Wing Commander - You can play this straight from the start, no learning needed really, and it's not open world like Frontier, but it's a bunch of missions with great campaign, story, and characters.
PC:
Civilization 3 (my favorite), Master of Orion 2, Starcraft 1 and 2, Stronghold, Gothic and Gothic 2 (amazing RPG's), Mafia 1 and 2 (always liked it more then GTA)... etc