In my Monarch level game, I just discovered Rifling and upgraded all my troops to Cossacks / Riflemen. No other civilization has this technology. I am the tech leader and clearly the strongest civ in the game.

There are 2 civs remaining on my large continent (the rest are on another continent). I'm prepping to launch an attack against the 2nd strongest civ, which owns about 1/3 of the land on my continent. The 3rd civ poses no real threat and only owns about 1/8 of the land.

It will be an easy battle with the 2nd strongest civ due to the fact that his defenders are mostly longbowmen. However, I have been struggling to decide which cities to attack first. Should I take out the border cities closest to my territory? Or should I immediately send my attackers deep into the heart of the civ to capture his best/biggest cities?

Or is there some other strategy that I'm not considering?

You will have a hard time reinforcing your attackers if they aren't strong enough to win deep in enemy territory. So the normal approach is to take out the border cities first.

However, if you are strong enough to wipe out his army several times over, the war will end faster if you target multiple cities at once.

Well, the way you've described it, I'd go for a plan of attack that makes logistics the easiest. If you have no real concerns about the attack stalling out at any point, you can probably feel free to attack in a straight line from your land into the enemy territory. That way, you can just keep sending in new troops without worrying about them getting picked off.

If you're in a situation where it will be more of a fair fight, I'd think about going for either a strategic city that will allow you to effectively weather a counter attack before rolling into enemy territory. The other thought in this case would be to immediately cripple the enemy economy/production base by quickly capturing the core cities.

Also, if you're thinking about not capturing all of the AI cities, but rather just making him or her a vassal, then I would certainly head right for the prize cities.

But, since it sounds like you're just going to stomp the AI into the ground, I would go for the border cities first.

I would agree on generating a tsunami and roll over their empire from the border onward.

Even with the tech and power superiority you are going to have war weariness issues start cropping up. Make sure your key cities have theathers/coliseums and ideally jails.

You can start the war now but focus your effort on drawing what troops they have onto your territory. With Cossacks especially you can do lots of damage to their stacks with minimal WW while getting your cities setup (if necessary) to withstand the push into their territory.

riflemen versus longbows plus a production lead means that you can probably build a large number of stacks that can each take a city, so it makes a lot of sense to attack on all fronts at once, in order to get it over with asap. Best would be to detect his main army first and make sure you can match that, but if it is riflemen versus macemen I wouldn't worry too much. Speed is important because you need to take the whole continent before your tech lead wears off.

In this situation I may split my stacks into A) Fast-moving and B) Slow/seige. The slow stack is likely the main force, and will work it's way toward my enemies' core cities. Even if you just have trebs, spending a turn to hammer away the defense will help a lot by reducing healing times for your rifles. The second stack will hopscotch around to attack newer cities with lower defense % or exposed counter-attackers and reinforcements.

Once you start to break through towards the core, the AI will pull in reinforcements and the remaining border cities will become more vulnerable to your fast stack or to your own reinforcement stack (since you are cranking out units while warring).

Without knowing how many turns it takes for you to capture each city(and the general lay-out of his territory), I'll just give a simple answer

Take out the desired cities at the same time as the border city

Make good use of the 2 movement of your cossacks