Artie,
1.) That "cable to plug into a house outlet" is going to be important. It has a three-prong power plug and so needs a grounded wall outlet. If you don't connect the ground, say because you used a generic replacement cable that didn't have the ground pin and you want to run TMCC locos, you won't get a good radio signal to the them and they won't operate well. The good news here is it sounds like you don't plan on running TMCC locos in the near future. Nevertheless I would still recommend investing in the proper power cable in case someday you wish to run them too.
2.) However, even more important is the cable needed between the command base and the TPC. Without this you can't control track voltage using the command set handheld. You'll be looking for a 6-14192 Serial Cable to connect the TPC to the Command Base in order for commands to be transmitted and received. Then you'll also need a 6-12194 Power Cable, or even better a homemade equivalent which could be a simple pair of wires between the output screw terminals on the MRC 270 and the input screw terminals on the TPC (as in the diagram). This will connect your MRC 270 to the TPC so that it can provide the AC power needed on the tracks in order to run the loco.
This diagram will help, if you replace the TMCC Powerhouse shown at the top with your MRC 270:
3.) This existing TMCC CAB-1 and Command Base set will be more than sufficient to control the TPC properly and run conventional equipment, and even TMCC if desired. If you'd like though you can invest in a CAB-1L and Base 1L but it will get you nothing extra with your conventional locos than what you already have unless you plan on running Legacy locos as well in the future.
Good luck and good running.
Mike