I find Axemen are what I use most also, mainly because I attack early enough where I won't have Swordsmen or Horse Archers and I'll attack at the weakest points, the idea is to cripple your rival in such a way as they never get any chance to pose a threat.
Phase 1 - 3500ish BC steal worker pillage ALL AI improvements. Call for Peace, with the AI crippled it might take 4-5 turns from when you move your unit out of their borders but they'll shortly go for it.
Phase 2 - Stack of 4-6 Axemen depending on their production capability round about 2000BC you should have at least 1-2 other cities up and they might have 1-2 themselves, likely only 1 though their third settler is probably being built! With your earlier war, you already have their territory maps, you should know where their copper/iron/horse resources are, they won't have had much (if any) chance to build Axemen or Horse Archers. It's unlikely you'll have Horse Archers or Swordsmen up yourself, but you should have a stronger military as they once again turned to the building path in order to keep up with you...and most likely they only have archers up to defend with maybe some warriors, so you take all but one of their cities, it's pretty much your choice which one to leave standing, but I'd start by denying them copper/horses/iron if you know where they are. 2 Axemen per archer is enough to get the job done, you'll likely lose you first and second Axemen but it's doubtful the Archers didn't sustain serious injuries to be mopped up by your remiaining 2. If you want to be sure bring 3-1 odds, no way they can beat those odds. Pillage everything they have consolidate and Sue for Peace take whatever you can, but you prolly don't have Alphabet or Currency yet so can't take either his gold or Techs, preferably try to have Alphabet about this time so you can grab one or two Techs before Peace otherwise anything he knows that you don't dies with him.
The important thing here is you'll likely now have 5-6 cities, a nice chunk of land all your worker techs researched and about 3-4 workers (2-3 of which the now permanently crippled AI built for you) Unless another AI went to war this early you'll have 2-3 city lead, a decent military, well developed land and likely the Tech lead. You can take out the next nearest AI or go builder from here, but you've taken a large enough lead to sustain you through to the end of the game.
Phase 3 (don't want to keep an angry neighbor around to ruin your rep with any other as of yet unknown civs) - In his current state there's nothing he can raise to save him from your next and final push, you don't even need Swordsmen just your battle Hardened City Raider 2/3 Axemen along with some reinforcing unexperienced Axemen for your initial losses to weaken his Archers then attack with your experienced Axemen to finish the job. Even if you wait until the turn of the AD's it's doubtful the AI will recover to the point of Swordsmen especially if you completed phase 2 strategically denying him resources. He won't get to Feudalism in time to ever pose any serious threat to your Axemen, you just need to bring 2-1 odds...
