I don't think there's anything lost by not playing previous generations; just buy the newest games. All the newest DS games (Diamond, Pearl, Platinum, HeartGold, and SoulSilver) can connect to each other.
The battle mechanics were hugely overhauled after the "Advanced Generation" (Ruby, Sapphire, Emerald, FireRed, LeafGreen), so I would not recommend starting with those games. If you do, it will take a little time to adjust when you start playing the DS games.
Pokemon Red, Blue, Yellow, Green, Gold, Silver, and Crystal cannot connect to the newer games, so if you think you will become attached to the Pokemon you catch and train in them, it's not a good idea to start with them. Pokemon from the GBA games can be "migrated" to the newer DS games, but you need to have a DS with both a DS and GBA slot (the original DS and the DS Lite).
In short, I suggest you start with either HeartGold or SoulSilver, as those are the newest games.
The Power of an attack directly correlates to how much damage you deal, because its presence in the damage formula is entirely multiplicative. So, an attack with 120 power will do twice as much damage as one that has 60 power. The same goes with your corresponding attack stat: a Pokemon with 100 Attack will do twice as much damage as one with 50 Attack when using the same attack on the same target.
STAB has operated consistently since Gen 1 so this applies to all of the games. It increases the Power of an attack by 50% if it matches one of your types. 60 becomes 90, for instance.
Technician increases the Base Power of an attack by 50% if its Power is 60 or less. So the most you get is boosting an attack at 60 power to 90. This occurs before STAB is calculated, so your Power would be 90 for STAB, boosting it to 135.
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The cleverly named Pokémon Dollar is the currency for Pokémon.