There are folks who are really good at finishing here. I am not one of them ;-). At the moment I have one successful stain under my belt, and I was not sure until near the end that it was going to complete it as planned.
I try to read as much about the product I am using. I also try to use products that are environmentally friendly, mainly because they all cure in my garage/studio/office, and I often apply the finish here as well.
I have some experience with water based dye stain. YMMV...I used a different stain and a different wood, but some of the principles should be the same...
One thing I would do for sure is raise the grain before applying anything. Get the surface a little damp. This will make the grain "stand up" so that you can sand it down. May not be much of an issue with a maple veneer and basswood back and sides, but I'd still do it.
The trick to staining is to get it even and not blotchy. If you stain before grain filling and/or sealing you run the risk of blotches. If you seal or fill first, you run the risk that the color will not be as deep. If you have a scrap of maple or basswood, I would try it both ways to see what works for you.
With the General Finishes stain that I used I followed the mfg's suggestion and put it on first. Because I was using an open grained wood, I added 1:10 some of their water based clear coat to help avoid blotchiness. I am guessing that you will like the results better if it goes on first, but this is really worth testing.
I put a coat of de-waxed shellac between stain and whatever comes next. I got this from McCreed. It makes a great sealer. While all shellac will yellow the finish a bit, platina is almost clear, and won't change the color much. Since I use a water based top coat, I need the shellac between the stain and the clear. Without it, the water in the clear can react with the stain and pull it out, particularly if it is wiped or brushed on.
It's less likely that an oil or solvent based clear will react with the stain, particularly if it is sprayed, but I have no experience with this, and haven't found a rattle can clear that I like. I can say from experience, though that oil based clear tends to get a deeper and darker yellow over time. I love this on a maple neck.