Before we get there, I thought I’d bring up the only random part of leveling up– hit points. There are a lot of campaigns out there, and they’ve each got a take on how to solve it. I think we’d all prefer not to have too many ones… especially for the first few levels when it really matters.
a) Three-quarters of max each level. This is the most generous guaranteed hit points that I’ve seen. [I have seen a few “just give max at each level”, but really, why make it a die type at that point?]
b) Use WOTC’s Monster design rules- average hit points per level (so 4.5 per d8 for example).
c) Roll the die. If it comes up a one, reroll it. Still pretty variable, but at least you’re not stuck with ones.
d) Roll two dice & keep the better one. While there’s still a chance of a low number (even a one), it’s pretty slim.
e) Roll three dice and keep the middle one. This cuts back on the extremes- both high and low are unlikely, so you’ll often have a mid range roll.
f) High minimum old school For the first ten levels, characters are guaranteed high hit points (reroll anything falling in the bottom half). From 10 on, the con bonus is eliminated, and it returns to +1,+2, or +3 per level, like old 2nd edition. (It’s an interesting tradeoff, but it doesn’t reflect 3e’s assumptions very well.)