I'm sorry, but as a top laner I don't disagree with you saying Garen is viable-- hell, I've lost to some in diamond. Garen is especially good for new players. But thinking about a build path so linearly especially for a new player is not a good idea.
Generally the brutalizer on Garen is a better first back. You can cs better and actually do damage. If you're against a very difficult lane there's nothing wrong with going full tank because that's what Garen does best, but I don't recommend going back for a giant's belt first except in a few cases. You'll lose lane just as much, only 400 health slower.
Take their team comp into account-- do they have something like a trynd top j4 jungle? Get ninja tabi, chain vest, and giant's best asap.
Irelia top? You're going to want that Giant's belt-- she is very difficult to itemize against and health is the best way to counter true damage.
Lulu top & amumu jungle? You still want that sunfire but don't even think about it until you have merc treads and a cowl or hexdrinker.
If you're not having trouble though there's nothing wrong with rushing that brutalizer. After that, generally build tanky and turn your brutalizer into a cleaver late game.
As far as gameplay goes, get a point in q and max e, fuck his lane up. Remember to cs as well as you can-- it's alright to use your q to last hit a minion. When you get a chance you can auto-q-auto-spin or q-auto-spin depending on your close you are to him, to put down the mad harass. Also remember, it's generally not worth it to go in for a q harass if he's standing in his minions (early game. late when you have armor it's not a big deal.). The minions will chunk you down pretty hard. Just focus on cs until good opportunities come up.