Was Kennedy's decision to send a man to the moon a good one? How was technology expanded through the whole process and how would it have continued to expand had the race not ended?
I'll cover USSR side.
First, "Space Race" in a narrow sense (e.g. sending men to the Moon and back) is a construct of western media.
Space program in USSR was not fixated on sending man to the Moon. It was just one of many goals and it wasn't a primary goal until USSR political leadership has realized importance of such event for propaganda. Ironically, it rather played against USSR, as hurried-up production of re-targeted Korolev's Н-1 lead to catastrophes - all 4 launches were unsuccessful. Primary reason was difficulties with synchronization between engines and timing of stages - led to instabilities in active flight.
H-1 has much more engines - 30 engines in 1st stage, 8 - in 2nd, 4 - 3rd, 1 - 4th and 5th than any other booster. So, in total - 5 stages and 44 engines. Monitoring and balancing fuel injection for consistent thrust was very difficult without microelectronics. For comparison, Saturn V has ~5 engines per stages 1-2 and 1 engine at stage 3. There were 2 other competing projects in USSR - UR-700 from Chelomey KB and R-56.
Originally H-1 was envisioned as a booster for super-heavy orbital station (75 ton) which would then assemble a manned spaceship for flights to the Mars and Venus.
USSR space program was focused on near space and long-term orbital flights to closest planets - Mars, Venus.
After USA astronauts stepped to the Moon, USSR switched to unmanned exploration - Lunokhod - robotic rovers were sent to the Moon and being remotely operated via radiolink.
As a result of H-1 failure, approach to heavy boosters was totally changed and Energia booster was created.
Sources
B. E. Chertok - Rockets and People. Three volumes describe in details all events of USSR space program.