Best strategy to collect cards?

To be honest there isn't a lot of ways to get new cards. Either buy/save gems and buy packs or get weekly event cards and recycle them for cards you need. Very good idea to focus hero's you have first. Try to build a maim deck for both plants and zombies.

Exactly what the smart fellow above said. I am so glad you decided to ask the forum before wasting your hard earned gems on a hero specific pack(s).
I have also been fooled by the draw of getting the cards just for the heroes that you have. But remember, that is temporary. Like @BlazinsZ said, every once in a while, you get super lucky and get a legendary and a new hero in a premium pack. I wish that every new player gets to experience that moment even once.
Also, as far as getting your fourth gargologist, that's smart and since we just got her for event, you know that crafting is the only way to get her.
But other cards, you should be aware of what is coming up for events that we aquire weekly, and those tou can save your sparks for things that you want or need.
If you ever decide to spend a few dollars, the best bet is to wait until you get an offer from ea. Usually when you move on to a new league they used to have a promo for extra packs if you get this much etc.....as someone who has spent real coin, some of the bonuses are pretty good, especially when you consider that you were planning on getting some anyways. And the deals are not for 50+ and all that, there's some decent offers.
But as free to play, if you are able to watch the ads, I have been told that it's around a 10+1 pack (1000 gems) a week, which is not bad.

Another piece of advice from someone who loves to learn the hard way....if you do craft cards, like I said before, make sure that it's not a card you may be getting in a month from event or whatever, and I have always been wary of crafting a fourth card to complete a set because I have on at least three separate occasions, pulled the same card that I crafted, only to have to recycle it for basically peanuts in comparison to how much we pay.
And the "free to play" label is kinda hard to lump every single player in one of two categories.
The pay to win players in my opinion, are those who buy the event cards only available for cash and use them for an advantage over players who don't have access to the cards.
Spending a few bucks to support a game you enjoy, and/or to just get a few packs is not the same thing to me