All champions, including the free ones on rotation, are balanced with each other (in theory); there is no real-money-only-champion with blatantly-boosted stats as is often in more P2W variants.
See Jarwain's comment in a sister thread.
Champions buy you playstyle, not straight advantage. At best, they give you options - but by the time you have played enough that a reasonably varied roster improves your chances to win, you have earned plenty to afford a varied roster. If you pay for hero it's because you want that hero, not because you need it.
You do, but the points needed to buy a new champ (I believe it's 6,300 IP) doesn't take too long to get.