There is, um, something I'm in the middle of writing that I think would probably be of use to you, but it's not ready yet and I'm not sure when it will be ready, so.....
But I can still answer your questions as best I can.
When should I start catching other Pokèmon?
Whenever you want really. Though in your case you'll want to catch stuff sooner rather than later, as Torchic has a type disadvantage against the first Gym.
What types should I catch and what should I avoid?
Basically whatever will help you defeat the major opponents in the games and cover all the HMs you need is one good way to look at it.
What should I even be doing in the game other than trying to defeat the four guys at the end?
Usually there's other stuff in the games for you to do besides get all the badges and defeat the Elite 4. Some are present in all or most of the games, like collecting as many Pokemon as you can, or trying to get a high win streak in the regional Battle Facility. Other things are in only some of the games, such as things like Pokemon Contests (Gen 3 and 4 games only) or PokeStar Studios (B2W2 only), for example.
Some people like to breed and trade Pokemon, others like to engage in competitive battling, while others still like to do challenge runs, etc. You have options, so whatever tickles your fancy.
How do I get really good and knowlegable of the game?
Look up information on things. Ask questions, no matter how small or stupid the question might seem. But above all, you'll learn a lot simply through experience. It'll take time, but you'll get there.
Regarding Nintendo handhelds.....
All versions of the Nintendo DS are (iirc) capable of playing Game Boy Advance games in addition to DS games, meaning that you can play Ruby, Sapphire, Emerald, Fire Red, Leaf Green, Diamond, Pearl, Platinum, Heart Gold, Soul Silver, Black, White, and Black2 and White2 on it (so basically Gens 3 through 5). The Nintendo 3DS is backwards compatible with DS games, so you can play Diamond, Pearl, Platinum, Heart Gold, Soul Silver, Black, White, Black2, White2, X, Y, Omega Ruby, Alpha Sapphire, Sun, Moon, Ultra Sun, and Ultra Moon (basically Gen 4-7).
The 3DS also has Red/Blue/Yellow (Gen 1) and Gold/Silver/Crystal (Gen 2) available digitally on the eShop.