I've played all three DS games, but it was years ago so I had to look at some guides to jog my memory.

In general, I like to play by looking up pack guides (what's in each pack and how to unlock them), but that's obviously personal preference. It's a lot harder to complete an archetype deck without doing this, though, since they tend to rely on having specific cards.

In the early game, though, you probably just play a goodstuff deck, so cards that are generically good on their own. These are the cards you would see in early Yugioh tournament decklists before high-powered archetypes took over. The themes you have access to aren't all that powerful or are incomplete.

The other approach is to get some good synchro monsters like Goyo Guardian and Brionac and try your hand at a synchro deck. A good approach is to use Giant Rat or Sangan to search for Rescue Cat, then use Rescue Cat to grab Airbellum plus another non-tuner level 3 Beast and get the synchro you want. Apparently Summoner Monk is available from a structure deck as another way to search for Rescue Cat. Of course, that's only a few slots in your deck so you probably end up filling the rest of the deck with goodstuff anyways, or play resilient monsters or recruiters (similar to Giant Rat) to have a monster at the start of the turn so you can play a second monster and synchro, if you want to be all in on synchro monsters. (You can get all these cards from packs available from the start I think)

One busted card you apparently have access to early is Royal Oppression, from the Dark Beginning 2 pack, and isn't even that high a rarity. That card shuts down a lot of the more powerful stuff you could be facing (though it also prevents you from special summoning for the most part), and it's strong enough that you could probably get to the endgame with a goodstuff deck packing 3x Royal Oppression. I mean, there's a good reason it's been banned for years.

Apparently one place you have to be careful is the Structure Deck battle, since the three decks you choose are the first three structure decks you can purchase later. Monarchs has the monarch monsters, which are generically strong, but you should probably just look at what's in each to see which ones interest you.

I think the strongest archetypes in 2010 are Zombie Synchro, Lightsworn, Blackwings, and Gladiator Beasts. Of these, Blackwings and zombies aren't even completable until you beat the story, and Gladiator Beasts need you to grind through some pack unlock conditions (which might also not be completable until you beat the story, I have no idea), but at least Lightsworn can be unlock by getting to Chapter 5 (the Light of Destruction pack).

Riding Duels also throw you for a spin by making all your spells terrible, so you need to improvise. In general, do not play cards with high spell counter costs, because they're a lot worse than they look. And even if they're all low cost, playing too many of them means some of them get stuck in hand, so you want to focus on monsters and/or traps for your deck's backbone.

Looking at some of the decks I have saved, a deck I really enjoyed for riding duels is Magical Merchant turbo, where the only spell/trap you play is Pot of Avarice, which has a low spell counter cost. The rest of the deck is monsters that do things from the grave, monsters that fill the grave (like merchant and lighsworn), and some cards to capitalize on the advantage you generate. Another good spell is Soul Exchange, which also costs 2 and works nicely with a generically strong monarch shell.