The first thing to look for is a MOSFET which has a specified performance at the best Vgs that you can achieve. This is not the Vgs threshold value but the lowest Vgs at which an Rds(on) is specified.
For the 2N7002 this is 5V so if working strictly to specification you rule it out.
The FDV301N has a max specified Rds(on) of 5 Ohms at 2.7 volts Vgs and an Id of 200 mA which should be suitable for you needs.
Devices like the AO3400 have even better performance and I think are on the JLC parts list.
Working any MOSFET in the unspecified Vgs range will not only have reduced performance but also be inconsistent between devices. This region is typically the so called linear region and used in low power amplifiers. However higher power switching MOSFETs are not designed to work in this linear region at all and may fail even when you think you are within power dissipation. This is due to the high power MOSFET being comprised of many smaller MOSFETs in parallel and too much dissipation for too long can cause a local burnout and a domino effect. This is also a factor if you do not switch the Gate voltage fast enough and spend too long in the linear region over time The MOSFET gates have quite high capacitance so drivers may be needed to give fast switching times at high PWM rates.