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HG will lightly introduce you to some of the new mechanics and features of Gen IV. HG/SS are easily the best two games of Gen IV. Also, you will relish the nostalgia of Gen II, especially if that was your favorite gen back when you were a kid. HG/SS also added a lot of fun shit alongside the familiar Gen II storyline. You'll have a lot of fun with the game, it's a 10/10 for sure.
Then, to fully delve into Gen IV, go back and buy Platinum. Platinum will give you the full experience of the Sinnoh storyline (over D/P), with extra Pokemon and a more badass plot. Some of the mechanics will feel kind of like a downgrade from HG though, since the touch screen isn't utilized as much, the menu on the bottom screen is replaced with a practically useless Poketch (so it's back to pressing a button to open menu) and there's no always-on button for Running Shoes (and the registered item buttons are also gone). But the gameplay will still be familiar. By the time you finish Platinum you will be versed in all Gen IV has to offer.
Personally, I'm skipping Gen V at the moment because I don't find the games interesting enough to spend $30+ each for one and a sequel. Maybe after X/Y come out. Speaking of, you probably should've bought a used 3DS for X/Y and better WiFi connectivity (if you wanted to use the Global Terminal). And it's just an overall better console, but I can see the logic in going with a DS lite since even used they're about $80 cheaper than a used 3DS.
Welcome back to Pokemon bro.