I used LM engine flush, injector cleaner and fuel system cleaner on 3 cars: 2006 Lancer (45K KM), 2003 CL7 (90K KM), Corolla 2009 (90K KM)
The effects on the Lancer and CL7 were phenomenal, and negligible on the Corolla. It's safe to assume that regardless of mileage, your 2001 Accord will benefit greatly. The engine flush results were remarkable; the engine was smoother and happier to rev.
Generally speaking, since you just bought your car and there isn't really a way to tell what's been going on, just change all the fluids. Brake, Steering, Transmission, Clutch, Coolant... You might want to check the condition of all rubber components, including bushings, engine/transmission mounts, suspension arms, shock mounts. Additionally, steering racks on hondas get damaged pretty easily, so check for play. You might also want to check the dampers, and control arms on the car, springs should be fine.
Also, have all your sensors on the intake and exhaust cleaned properly(remove and clean) - should be done with care. Also have the catalytic convertor checked for condition. This should greatly improve engine response, performance, fuel economy and idle.
Besides the steering rack, everything else is pretty inexpensive and can make a great difference in the way a car feels and performs.