But you give up your weapons when you come to Ceasars camp, right?
Only if you give them the chance to take them.
Honestly, the most straightforward way to do it is guns blazing from the outset. The only guys you really need to worry about are the Praetorian Guard in Caesar's Tent, and they'll happily wait inside while you shoot up the rest of the camp. Once you've done that, make a minefield (the more the better) outside Caesar's Tent, duck inside, lob a grenade to get their attention, duck back out again and leg it so you don't get caught in the blast. Then just keep moving, don't let yourself get swarmed, and pick 'em off with whatever your best gun is.
My other companion is Veronica, in a good powerarmor and her standard fist. Can her fist be upgraded/replaced with a better weapon?
Yep. She prefers unarmed weapons, give her a ballistic fist and she'll wreak havoc with it. I think she'll use some energy weapons at a push too.
You might have a job trying to keep your companions alive if playing H/C mode though.