This is one of the most useful equipment decisions in home coffee, and the answer depends almost entirely on how often you brew.
The case for manual
Hand grinders punch dramatically above their price because they put nearly all the cost into the burrs themselves. There is no motor, no electronics, no power supply, just the grinding mechanism. A $150 hand grinder will out-grind most $300 electric grinders on burr quality and particle distribution.
The downsides: time and effort. Grinding 18 grams takes 30-60 seconds of physical effort with most quality hand grinders. For a single morning cup, that is fine. For three or four brews a day, it becomes annoying.
The case for electric
Convenience compounds. A grinder that takes 5 seconds instead of 60 changes how often you brew, especially for impulse cups during the workday. Electric grinders also let you do back-to-back doses without arm fatigue, which matters for couples or households where multiple people brew.
For espresso specifically, electric is hard to beat. The fineness required for espresso makes hand grinding tedious, and the consistency demands push the cost of a capable hand grinder up to electric territory anyway.
Specific picks under $200
Manual: 1Zpresso Q2 ($80) for pour-over only, 1Zpresso K-Plus ($170) for pour-over plus espresso, Timemore C3 ESP ($130) for both with great value.
Electric: Baratza Encore ($170) for brew only, Baratza Encore ESP ($200) for entry espresso plus brew.
The hybrid approach
Many serious brewers own both: a quality hand grinder for travel and pour-over, and an electric for daily espresso. If you anticipate using both methods seriously, this is the most practical setup.