i would use some white-spirits on a cloth and rub-down the hand-rail vigorously, these often get very dirty from peoples hands. Make sure to get off as much dirt as possible. If they are in a bad way, a sanding might be in order. After applying the varnish, you could put on a coat of clear varnish to protect it and give it a bit of shine if thats to your liking.
Id undercoat the spindels and give it a coat of the satin, will prob need 2 coats of the satin though (you will see if it covered ok or not). If you are using the previously mentioned paint, you won't use the undercoat, just 2 coats of that paint. I dont think you need to sand the spindels, just give them a rub with the cloth. You can sand them if you want to and it will give the paint more grip.
make sure to mask off on the carpet, do a double mask i.e. two lengths beside each other, which will give you twice the width. Then put down your painting sheets and pull them back slightly when you need to access the area where the carpet and stairs meets.
Stairs done the way you are doing them look great IMO.