Air or electric. Propane makes it easy if you can get it in there. You won't likely find one to rent.
I wouldn't run gasoline equipment in a basement but to each his own. Definitely don't do it solo with gasoline, that's a good way to kill yourself. CO poisoning is insidious; you will begin making poor decisions and will likely not recognize that you are close to sitting down to take your last lunch break. Even with a buddy, the other guy will lose cognitive function so what good is that?
You can't have too much horsepower. Cutting by hand is tiring, might as well cut fast. Removing a bunch of rubble will not be fun. Digging will not be fun, nor will carrying out the buckets. If it's an old building, the substrate is probably junk rocks and garbage so you'll be hauling that out probably to get stone/sand in there.
With the walk behind, I can hydrate with Dunks while the saw does all the work.
This next one I cut by hand, with a 4 horsepower air saw, 7" max cut depth. Turned out there were three slabs, all stacked on top of each other, for nearly 10" total thickness. Old mill building.
Depending on how big this project is, might be a good candidate for hiring out.
If you're going to cut the perimeter and then try to drill/break, rent a rock drill and a ninety pound paving breaker. Drill a series of holes to segment off the size piece you'd like to remove, then put the point of the breaker in one of the holes, at an angle. It should break. You could just saw them and that would be faster but you'll need to overcut, even then it will need to be broken off on the wall side of the cut because the blade will not reach the bottom corner and you can't overcut that side even if you wanted to. So depends if overcuts are okay or not.
Beware the rock drill will be hungry for plumbing lines, they drill fast. If you can't handle 150 to 200 lb pieces using bars to remove, you might as well break it into rubble and put on gloves to take it all out by hand. Get the buckets.