I started over around level 35 and started playing a ranger-esque character. No magic at all. Been enjoying this character just as much, if not more.
Play around with the character. You could always "bank" your perks for the first 5-10 levels if you really want to maintain some flexibility and avoid a "redo".
I didn't mind restarting, so I was taking perks as I went along to help build my characters.
I'm a "veteran" gamer too, going back to the original TES PC game and a few before that.
Skyrim does a pretty good job of being "open" architecture with respect to characters.
