I had the same problem initially too, Welchy until I put index_home.css into includes/templates/classic/css. I also got quite confused with naming everything, but this is what's now working for me...
In admin:
Configuration > Layout Settings > Banner Display Groups - Header Position 1 ... Leave blank (the same for position 2 & 3)
Configuration > ZX Slideshow > Banner Display Groups - Slide1 ... slide 1
Configuration > ZX Slideshow > Banner Display Groups - Slide2 ... slide 2 (Slide3, slide 3... Slide4, slide4 etc.)
Tools > Banner Manager > New Banner
Banner Title: (enter a title. This will be displayed with the image)
Banner URL: (The link you want the image to lead to (if any))
Banner Group: (type 'Slide1' into the field below the drop-down menu).
Image: (mine is set to /home/sites/MY_SITE/public_html/banners/slide1.jpg)
Image Target (Save To): (mine is set to /home/sites/MY_SITE/public_html/banners/)
Click 'Update'
Repeat the 'New Banner' steps for each image, but increment the 'Banner Group' and 'Image' each time.
i.e.
'Slide2' & 'slide2.jpg'
'Slide3' & 'slide3.jpg'
etc.
Then try altering the themes (Configuration > ZX Slideshow) to see which you prefer.
Well, this works for me. Hopefully it will for you too.