I agree that the paint probably just needs some lovin to start shining again.

When I first started learning some of the basics of detailing, I used my brother's old beater truck as a guinea pig and this is the change just by hand.
The truck had sat under a tree and was covered in moss and algae before he inherited it from our great uncle.

Before

After


You should be able to bring it back pretty decently. White paints, if I recall correctly, are often single stage with no clear coat anyway, and are very VERY hard (compared to black/red) so you might need to work on it a lot more.

 

stage 1: take it to a professional detailer where they can use compounds to remove the scratches via machine and or /wet sanding to see the initial result.

 

That's good advice about having a pro assess the condition of the car.

Just about everyone went to clear coat refinishing by the end of the 90's. There might be a couple single stage cars still out there but your Honda should have clear coat on it.

If you start buffing or sanding on raw paint there's a good chance your burn right through to the primer, or worse, bare metal.