The vehicle ran fine one day and the next it just wouldn't start. I replaced the battery and the plugs and got nothing. It is turning over, getting fuel, and getting spark, it just refuses to start. I also checked the fuel filter and all my fuses.

Replace the Ignition Control Module (ICM) and coil:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-4.html#post265896

This presumes the CEL comes on and goes off normally, when the ignition switch is turned to ON (Position II).

Would it be easier to change my distributor if I can get one at good price?

Only if you can afford to buy a genuine Honda distributor. Aftermarket distributors for Hondas are not reliable. To keep the cost down, you could buy a genuine Honda distributor housing and install an aftermarket Ignition Control Module and coil. No problems with aftermarket ICMs and coils.

If I replace the entire distributor why would I still need to change the ICM and coil?

You wouldn't. I think my answer was pretty clear. You can install a complete genuine Honda distributor, which includes the distributor housing, ICM, and coil. Otherwise, you can buy just the genuine Honda distributor housing and install an aftermarket ICM and coil, to keep the cost down. Complete aftermarket distributors for Hondas are not reliable. Your choice.

Sorry I just realized in your first response that you asked if the CEL light came on and went off. The light comes on and you hear the fuel pump but the light does not shut off

If the CEL stays on, the problem is with the ACG (ALT) (S) 15 amp fuse, in the under dash fuse/relay box; ECM (perform the K-Test); main relay; or the ignition switch. Perform tests in that order.