In the cash games I play in most, 40-50 BB is the typical minimum initial buyin, and 150-200 BB are the typical maximums.
Either half the big stack or match the big stack are typical maximums once the game gets going.
(Note: I’ve never seen someone come in so late and so hot that they want their *first* buyin to be the “match” size. If someone arrived three hours in I’d probably hold them to the 200 BB for their first buyin — if only to disincentivize late arrivals. Never thought about it before.)
Top-offs/add-ons can be done at any time, up to that game’s max.
Now…
As host, I prefer either all rebuys be the initial max, or not more than half the big stack. Reasons:
It can be hard, longterm, to keep the lower-bankrolled players coming back if, when they are running well, they always get ganged up on by wealthier players matching their stack and playing BINGO against them, knowing the lower-rolled player will play too tight.
You could say that’s just poker. And that the lower-rolled players should want others to play too loose against them when they’re up.
But again, as a host, I feel some structural protection is important to prevent the disparities in my regs’ rolls to create a hostile or unlevel field. Allowing “match the biggest stack” can lead to uninteresting, all-aggro play, and chase everyone but your richest 3-5 players away over time.
IMHO it’s also just a more interesting game when you have to *earn* a 500 BB stack… rather than just buying one to bully less-rolled players, because the money doesn’t matter to you but it does to them.
Personally I can rebuy and rebuy as much as any of my regs, but there is at least 60% of the roster who are coming with no more than 2-3 initial buyins in their pocket, and leaving if they use those up.