Dunno about Pegg's version, but the original Scott was born in 2222, was commissioned into Starfleet in 2242; you can say he entered the Academy that year on a cadet's commission, or you can say he graduated from the Academy in that year -- if the latter's the case, he entered Starfleet at 20, and if the former is, then he'd have to have entered at sixteen, assuming the Academy's four year. Most indicators are that it is.
If you go by the novel Kobayashi Maru (non-canon but his story was cool), then he spent a stint in Command School before moving over to Engineering, so you can guess that maybe he went in at 18, as would be pretty standard I think even in that century, but didn't end up in the Engineering division until he was 19 or 20. Makes sense to me, as it's not exactly standard practice in any naval force that I know for the Chief Engineer to also be the second officer, carrying out dual jobs like that.
Either way, he's about 44 when TOS starts, making him twice the age of the youngest confirmed member (Chekov). Kirk's age was also confirmed in canon, at 34 (right?), so you've got quite a good spread of ages in the original cast. The rest are conjecture, but solid conjecture based on actor's age and plain old common sense.
As to Pegg...
I'm sure I'll be argued with, because there are plenty of folks lurking around who jump on every chance they can to argue about it, but I don't plan on coming back to this thread (in other words, don't bother, I'm entitled to an opinion, you're entitled to disagree and I'm entitled to ignore you), so... by all means.
I don't think Pegg can do it. A lot of folks forget that there was more to Scott than just the stereotypes they admittedly abused in TOS; he did have moments of genuine sharp, where he was a very effective commander. He definitely had moments where it showed he was smart and canny both, and that there was more to him than just deus-ex-machina. One thing you never doubted about him was that he was capable of leading his people, and even commanding the whole ship, even when he was sometimes saying something kinda on the stupid side.
(Unless a woman was involved; then all bets were off and he was a total twit. But that's a neat character flaw.)
There's just no way Pegg could ever play this character. Scotty was a whole lot of Jimmy Doohan, a whole lot of untapped potential, a couple cheap stereotypes and an accent, and it was Doohan who gave him those moments of intensity and canniness. It was definitely Doohan who gave him a lot of his quirks, both good and bad, and heck, it was Doohan that gave him his own middle name. You can't ever expect anyone else to take a character so completely belonging to someone else, and do a credible job of it.
Honestly, I don't think anyone could have. Really, I feel that way about all of them, but most strongly about Scotty, and certainly about Jimmy Doohan, who was an excellent character actor on stage, radio, television and even film. And an excellent human being besides.
No matter how much Simon tries, the best he could pull off is to not botch it too badly; he can never make this role his own, it firmly belonged to Doohan. The worst he could do would be a pretty cheap laugh, and very little else. Either way, he'll never be Scotty.
Which is fine with me. The one already there has always been good enough for me.
TL;DR Summary: Scott was about 44 in TOS, Chekov was 22, and I don't think Pegg stands a chance, even if I like him everywhere else.
