The ES-3 isn't supposed to have veneer, just basswood with a decent grain pattern on the outer ply. Having said that, the outer ply isn't that thick, but I'd say it is thicker than the 0.6mm veneer on the other kits. So it will take some light sanding, but if you see my ES-3 build diary (link in my signature), then you'll know that I did manage to sand through it in a couple of places (on convex body curves where it's easy to over-sand). Also I found that too much sanding weakens the grain pattern.

I'd definitely mask the binding, whether staining, spraying or a mixture of the two. 6mm 3M vinyl pinstripe tape is your friend here. I've just used it to tape up my binding (for the 3rd go at spraying) and it's really easy to use, bends nicely rounds corners and curves without any crinkling. Some (but far from all) binding seems to have small cracks in, which does absorb stain and this is difficult to remove. If you spray, then scraping the binding is in theory easy (when you look at the YouTube vids), but a lot harder in practice to the beginner. Also if spraying and scraping, don't let the paint dry for too long before scraping. Maybe wait a day after spraying the last colour coat and then scrape whilst the finish is still fairly soft. The longer you leave it, the harder it is to scrape.

When spraying or staining, always fill the body cavity with something - I used a mixture of bubble wrap and newspaper - to stop paint or stain getting on the interior wood. Also do this when wet sanding your finish (as the coloured water can also leave marks).

You could finish the body and neck separately, then fit the electronics into the body and then glue the neck on. The neck cavity gives a lot of access to the interior. You'd then just need to touch up any gaps around the join areas and just go over that area again with whatever final coat you decide to go with.

However, as it is a full hollow body, it is very easy to get the pots in through a pickup hole - no messing about with F-holes. Whilst plastic tube can make it very easy to do, I've done hollow and semi-hollow bodies before just using cotton or thin string. Having someone to help you hold things at this point is a great idea and makes things a lot easier - though you can do it by yourself.

I've made my life a little easier by enlarging the jack socket hole and fitting a Les Paul-style jack plate instead. This means that I can pull the jack socket through the hole and fit it onto the plate and screw the plate on from the outside. It's easier than trying to screw the jack socket on tight from the outside and allows much better tightening of the socket, plus making it easy to re-tighten in the future.

I also had to wait a few weeks before my neck joint fitted properly, probably due to the changes in temperature and humidity as it travelled half-way round the world to me and sat in various warehouses en-route. Yours has still travelled a few thousand miles. If you've got small gaps round the edges of the joint, then you may find it all sits better after a few days.