So I start with the nude base and I use texture painting in blender to simply paint onto the model. I know that sounds scary but it's really not that hard. the main 3 steps are :
1. Solid blockout
2. Paint shadows/dark areas
3. Paint on the highlights
Once you crunch it all down into ps1 style it usually hides any blemishes you may have added.
If that's too much you can also add a second material for the clothes, create the textures first, then align the UV maps to make them fit.
One last thing that you can do is texture baking, which I also do a lot. Take a high poly model that's finished, align it to the PS1 mesh, and if you bake the diffuse only it will basically copy all the detail and textures to your PS1 model. The downside is that you need a highpoly model for that.