I'm going to vote for IPB too. It's a very good premium software but I think that the price there is a bit high. As a free option MyBB would be excellent. Just need to install the MyAlerts plugin and find a good theme.
I'm not a fan of IPB, to be honest. I just feel that it's a bit too bulky and large whereas a software like XenForo is great. But if I had to choose between IPB and MyBB, I would probably go with IPB. I think you just get a different feeling with a paid software and it's better to have it than MyBB.
From my experience IPB is much better from MyBB, I do use MyBB, for me it lacks a lot of functions and the functions it already has are mostly worse from similar function in IPB. The great thing about MyBB is community, you can find plenty of addons and styles for your forums, MyBB community is bigger than IPB, since Mybb is free and they make every public addon for free, in my IPB community I noticed few paid "hooks" which is not a problem for me because everyone wants to earn something for their hard work. But overall IPB wins for me, I don't use it for that long but so far experience is great
I have been using MyBB for more than 7 years now but it's not responsive. So, I will have to pick IPB over MyBB for that very reason. These days, many people are using their phone to access websites.
So, the forum should support responsive content.
I suppose we could use a responsive theme for it but still, that's too much work.
I am running a forum on MyBB, it is still a small community but I am perfectly satisfied with MyBB. I have never used IPB as an owner. However, I have used it as a staff and I think it is a nice script. Sadly, it is one of the most expensive scripts. You not only pay for the scripts for all add ons.