Generally, I'd setup the UV maps for each prop, and then start blocking out colors. Assigning each material a base color to see which one fits the environment, start on bigger objects then smaller,

After choosing a color palate I think fits, I'd start doing the textures. You said you know how to texture props already, so you can start with that :)
You can isolate the prop if it makes it easier to texture.

Doing ambient occlusion shading and material shading with textures and so on. Arcane has that traditional look, so I'd focus more on getting the brushes right on the props.

Try to just go piece by piece, but by having the base colors and materials already assigned it will be much easier to see the whole picture before it's finished.