Reapers are not a good idea. Practically every Protoss build will have a Stalker out by about 4 minutes and 5 seconds. (Unless they skip their cybercore and go for a fast expand). The fastest Reaper will spawn at about 3 minutes and 50 seconds (if you skip your first marine)... but you also have to add the travel time to get to your opponents base... on a small map it will take 30 seconds to get to your opponents base... on a large map it will take much longer... So usually by the time you get there the stalker is already there, and your Reaper 1) can't kill the stalker 2) is denied any scouting 3) wasted your barracks production. You can almost produce 2 marines for the price of that 1 reaper... so essentially your army is much weaker now just because you produced that 1 Reaper.
My best suggestion against a protoss for a large macro map would to be no gas fast expand.
Build SCV's non-stop, get your supply depot, barracks, orbital as usual... but don't get any gas. Produce marines and build a command center at your natural, place one bunker down in front of your command center and you'll be fine. Put one marine in front of your bunker or you can have it go scout and check for proxy pylons which might indicate a 4-gate push. Depends on how much scouting information you were able to get... (did you see more than 1 gate? did he save his chrono energy or was he using it on probes)
My best suggestion for an aggressive protoss that you also want to be aggressive against would go with a fast rader/rine combo with conc shell.
-barracks (build 1 marine then make reactor)
-barracks with tech lab
Heavy 2 rax aggression if timed right will stop protoss early aggression. Hope this helps, good luck.