Concrete porch demolition
I'd budget two or three days if you're by yourself. The stairs will likely be the most time consuming. The slab is going to be obnoxious primarily because it's over that hole. It doesn't look like you can fit staging in there, and a ladder is problematic because falling debris can knock it over. I assume the dangers of demoing the slab while standing on it are self-evident. It's hard to say without a good look, but I suspect working backwards and into the door may be the best bet.

The Tools


Three pound hammer - You're going to want a short-handle sledge for chisel work at some point, and three pounds is a good compromise. Nailing hammers (12-26 oz) are a bit too light and five pound hammers are a real workout if you're not used to them. 
Masonry chisels, two - You'll want flat and pointed, the exact sizes and shapes depending on budget and what's in the store.
Goggles, not optional - No way a chip doesn't hit you in the face at some point.
Long-handled sledge, optional but pretty damn handy 
Angle grinder, a big help - Really the cheapest tool to reliably cut both masonry and steel; something in the 4" size with both metal and masonry cutoff wheels. The fibrous disks wear out quickly, but they're probably a bit more forgiving than the diamond wheels if you run into steel accidently. Otherwise you'll want at least a hacksaw or reciprocating saw to deal with the rebar.


In addition to the short list you'll probably want to rent an electric demolition hammer for one day. Apart from the obvious labor savings it's good insurance for the stairs; you won't need to buy more tools if they're exceptionally difficult to break down.

The Plan


Bar the upper door. You really should put a railing on the outside across the opening, but I get that it's brick and you don't live with an OSHA inspector. You should still consider at the least a sawhorse inside blocking the door so nobody marches out forgetting that the deck is gone.
Score the slab along the house. Make a shallow cut parallel to the wall to encourage the slab to break rather than drag bricks out of the wall.
Carefully remove the slab. It looks like your best bet is to work carefully from the stairs, ground, and doorway to chip away at the concrete. Just don't work underneath or on top of it!
Once the slab is reduced enough that you won't kill yourself, cut off any large remaining pieces of steel. At this point the stairs and columns should be freestanding.
The stairs look to be free of the house so removing them is a simple matter of breaking them into small enough pieces to lift. Electric hammer, cuts and a long-handled sledge, judicious application of a pointed chisel are all valid approaches.
Score and smash is your best bet with the partition wall, though it looks like a pointed chisel in any of those cracks would brink half of it down. If you want to save a portion it's best to work your way down carefully removing small pieces.
The brickwork can be dismantled with a masonry chisel applied to the mortar. Running a cutoff wheel along the bed joints can help if the going is too difficult.