Drums are great at holding large loads, but that does not infer that they are the best for stopping power.
Since when are truckers concerned about stopping for bambie, or barbie who just cut him off? There is a reason 99.98% of semi tires are retreaded. For the record, discs require a lower initial pressure to activate, but higher rising rate for linear stopping power increase. Drums are the exact opposite, which is one reason why discs are prefered for ABS. It's also the only real reason the prop valve is different, it allows the rears more initial pressure until they engage.
The best upgrade for the civic is not rear discs. First you upgrade to GSR/LS/EX hubs+calipers, 10.3" rotors, and 7/8" Master cylinder and brake booster. That's far more effective than rear discs. Some people will say pads is all you need with CX rotors - they may also tell you that D15 just needs a header to open it up...
If you want to get "serious", you get ITR/Prelude VTEC/Accord Wagon calipers for the front with 23T brackets. Mill the mounting spots ~1/8" (IIRC I did 0.128"), get some 10.3" rotors or redrilled 11.1" if you use GSR/LS/EX hubs, and slap them on. Add at LEAST a 7/8" MC+BB, ideally a 15/16" or 1" teg version. 14" rim minimum for the 10.3" and 15" rims for the 11.1" combo.
With some decent pads, it will be linear as hell, have much higher fade resistance, but still rip your teeth out if you have a moose jump out in front of you. And I'm not saying that like "oh my unsprung 3-puck xtreme duty PP clutch is easy to daily drive", I mean my grandma could jump in the car and stop well enough in the rain for a deer as she would for a stop sign.