I've just started playing this, which I suspect is well-known to strategy fans. I'm enjoying the combination of high-level management and real-time battles (I'm doing the Byzantines on Easy mode as a warm-up but I've still lost a few). Any tips or talking points?

For general strategy, you want provinces to specialize in particular kinds of production (archers, cavalry, trade revenue, naval, etc.) You can't garrison everywhere in strength, so build up fortifications on your borderlands to withstand sieges, and have mobile armies ready to respond to attacks on their regions.  Use those four and five-star generals when you have them.

In battle, try to keep a tight rein on your units even when the battle is going well. Things can go south real fast if your units are dispersed and uncoordinated when your opponent rallies or brings in reinforcements.

As the Byzantines, you'll need lots of light cavalry once you start messing with the Arabs. I had a couple nasty surprises when I marched experienced and well-balanced armies into the Levant, only to be swarmed by hordes of horse archers.

I keep on getting generals knocked off by assassins. Is there anything I can do to prevent that?

Hmm, I don't think I've ever had a leader killed by an assassin. Does it tell you who sent the assassin? If so, wipe them from the face of the earth!

Seems like I used assassins to combat assassins. I would have them wander the country side and kill whatever assassins they bumped into.

I might be thinking of Rome: Total War, though, been some time since I've played.

The AI is never your friend, even if they are your ally they will take the first opportunity to stab you right in the effin' back. Never ever leave an unfortified province on a border with an ally, they will break treaty and attack you at the worst time.

Somewhat belated response but the difficulty settings make a huge difference.

At VH/VH you can no longer use the autocalc button with any confidence (although you'll still handily win most battles you fight on the battlemap due to the criminal stupidity of the AI) and you will eventually be attacked by everyone.

But at any other level it is no challenge at all (if for instance you are losing generals to assassins at Easy then you've obviously not had most of them killed in battle or survive to accumulate the various battlescarred traits that protect against assassins like I have).  

The two basic strategies are blitzkrieg (attack not all those pesky rebels but your closest neighbour and take all his settlements before he is strong enough to stab you in the back - particularly important if the neighbour is Milan or Venice whose troop rosters are particularly threatening in the early and middle game) or what I call slow burn (only attack rebels - and non-catholic powers if you are catholic - ally with everyone, carefully garrison your settlements to deter attack and focus very heavily on economic buildings and trade).

Even at VH/VH I can usually slow burn through fifty or more turns without being attacked and so accumulate enough wealth to be able to quickly arm up when the neighbours finally do turn on you.
 
Slow burn also lets you build a good relationship with the Pope (whereas blitzkrieging other catholics will quickly get you excommunicated) so that when other catholic powers do attack you can launch crusades against them.

Personally I find slow burn much more satisfying for most factions - fight out every battle and siege, avoid expanding too fast, use diplomats, spies, assassins and merchants etc to the full.

Plus when you get 30+ provinces all the micromanagement of settlements becomes a chore.