Do you have a play it again sports near you? Seems like the one near me frequently has used junior clubs, it might be worth a try.
I don't have kids, but I did start playing when I was one. Here's my perspective:
My dad started me on par 3 courses, and he always made me focus on the shorter clubs. Aside from screwing around with fairway woods at the range, I don't think I actually hit a driver (or 1 wood as they were called then) "in anger" until I was a teen. In retrospect, I think this was stupid; sorry dad, just because you shank your driver into the woods doesn't mean I will... He also started me on regulation courses way later than I thought I should have (I was probably 12 or 13 the first time I played a par 72, and that was with my uncle.) I guess my point here is that I think I was held back from a few aspects of the game and I think that was more of a hindrance than a help.
Growing up, I received several sets of hand me down clubs from various family members that were cut down and re-gripped, although I've read this isn't recommended because of the way the shaft flex changes when it's shortened too much. Then again, it seems like nobody outside of tour pros gave a shit about that kind of stuff then.
My biggest regret was that I didn't receive more professional instruction. If your kids do show an interest in it, I'd highly recommend you get them some actual private instruction (not just golf camps or group lessons.) I also didn't get the opportunity to play high school golf (school didn't offer it) but I feel like that would have been a huge benefit for me.
Good on you for getting your kids started now. It's really an activity they can enjoy for the rest of their lives, and from what I've seen people that started as kids have much more fun with it and get way less pissed off than those that started later in life.