So this is the type of question where you'll get a bunch of slightly different answers based on playing experience and player's style, which is good because you'll also gain an insight into other's approach to the game.
So given that money isn't an issue for you here, I'd always say buy in to cover the biggest stack. If not possible, i.e. max buy-in like in your case then buy in the most you can.
What are the advantages of playing with a deeper stack in a live cash game (and is it worth the extra money)?
Well frankly, in my opinion, poker is best played when you have all options and styles available to you so you can switch gears and play to counter what your table is doing. Having a deeper stack is the only way you can guarantee this, when you're short stacked, your options are limited, you always have the risk of a bigger stack bullying you and forcing you to fold hands, etc.
By having a deeper stack you can be the bully, you can dictate the flow of the game, you have all your options available to you, you can play your entire hand range, etc. Plus when getting it all in, would you rather double up to 400$ from 200$ or, if you were in for less, i.e. $100 to $200?
So is it worth it? In my opinion, absolutely yes it is worth it every single time. If you're playing for fun, the bigger stack allows you to make goofy plays and have a bit of fun, run some bluffs, etc, you have all your options. If you're playing seriously, again you can play however you like, you can place stacks under pressure, put them to difficult decisions rather than you being forced to difficult decisions.
How many BB do you buy in for when you play live?
Depends entirely on the table max and the largest stack on the table. I will always, at the very least, (if allowed) have 100BBs in front of me. Provided the biggest stack on the table isn't something ridiculous I will buy in to match or cover them. Again this is as I mentioned above, I want to be able to stack any and every player.
What are some reasons to buy in for less than maximum?
Short stack poker is a very easy game to play, you frankly don't have chips to get yourself into weird, awkward spots, where maybe you're your facing a 4 bet all in on the river with some goofy hand because you tried to run some ridiculous play (pretty sure we all have done this at one point :P).
So as to when you should buy in for less, you should buy in for less if you're more comfortable just getting a good hand and playing solid ABC and don't want weird spots against other big stacks. Short stack poker again leaves you with much simpler decisions to make, often if it's made it to the river and you're still thinking of playing it's likely going to be a shove.
Another nice reason to play short stack poker would be that you also can take options from bigger stacks and force them to thread carefully. If max buy-in like your case is 200$ and you have 100$ stack, a shove would absolutely hurt the bigger stacks, and as such they should thread more carefully against your shoves... well in theory, ultimately most people play sub-optimal poker, especially in lower stakes. As such stack size might not even matter to some people, but rather $ value might be more important to them.