God said:

Ok, so two questions here about the mastery branches:

1) I know for clan boss, the goal is to focus primarily on the offense branch first to get to Warmaster or GiantSlayer. Does the same apply to arena champions, or is there something else that is preferable for arena?

2) After capping on the offense chain, is there a particular branch that is preferable over the other when it comes to support or defense, or does it just depend on the champion? I don't see anything in particular on either of those branches that seems like it would be a "best choice" overall, but figured I would ask.

1. For arena champions, the answer is, it depends. If you are up against tanky characters, wm of gs will likely be better, whereas if you are up against squishier characters, the +20% crit dmg will be more beneficial.

2. Again, it depends, does your champion has useful debuffs? Then go support and get accuracy/debuff duration increase.

God said:

Ok, so two questions here about the mastery branches:

1) I know for clan boss, the goal is to focus primarily on the offense branch first to get to Warmaster or GiantSlayer. Does the same apply to arena champions, or is there something else that is preferable for arena?

2) After capping on the offense chain, is there a particular branch that is preferable over the other when it comes to support or defense, or does it just depend on the champion? I don't see anything in particular on either of those branches that seems like it would be a "best choice" overall, but figured I would ask.

I honestly don't know if we're allowed to post YouTube links (I hope we are) and your question is a good one, but it also has a lot of answers. 

I'd suggest you check out SKNOVA's full guide on Masteries (he will discuss almost every node and also tell you when to use what). 

NB! It's an hour long video, so when you don't have the patience, just scroll through it to the spots where he will discuss the nodes you're interested in! :)