IT'S MATH TIME:
So, leveling from 1-30 nets you 3 free champs, Ashe, Garen, and Brand. You can also get Alistar and Tristana for free, so that's 5 champs. Now, with the level 1-30 rewards you get 14 champion shards of various levels. Counting the level 5 reward as 1350 champion shard, you get 6 1350 champion shards, 3 450 champion shards, 3 3150 champion shards and 3 4800 champion shards.
Now, let's assume that you hate every champion shard you get, and you decide to melt them all down to BE. You'd garner 6660 BE from all of that. Now, you add the various BE rewards you get from leveling, and that brings your BE total to 19310. Which is enough for you to buy 42 450 champions, or 14 1350 champions, or 6 3150 champions, or 4 4800 champions, or 3 6300 champions.
So, if you simply upgrade the shards you get, you'd get around 20 champions, and then whatever you got from your glorious capsule. You'd also have some amount of BE left, but I don't feel like calculating that. If you didn't and instead decided to buy the champs you wanted specifically, you would be able to afford less, but quality over quantity amirite. If you add to that the current 14 free rotation champs, you are looking at potentially 34 champions without spending a dime on the game, which is pretty good.