Most brass sold as household decorative trim is straight apha phase material, and not very well suited to salt water use. You'd be better using what we know as bronze in the UK, and I think you know as Red brass in the US. Otherwise "Naval Brass" which has 2% Molybdenum in it is good if you can get it. Otherwise, don't dismiss a marine grade of aluminium alloy - it works very well, and looks fine too, and needs no cleaning.
Most people seem to go for about 1/2" strip for a boat of that length, and if you can get it in straight lengths of around 12' long, so much the better: it will make putting it on neatly easier.
No need for any fancy joints: just cut it off nice and cleanly and square, and make sure the joins don't come anywhere likely to take a lot of knocks like right at the bow or stern.
Screws need to be quite big: I would suggest a minimum of 0.75" long, and Number 8 gauge in UK terms, which is just over 4 mm shank diameter. The length does depend on the structure you're screwing into: you don't want to go right through the hull or deck material.
Screw spacing isn't critical, and there's something to be said for making them a bit closer at bow and stern, and wider elsewhere, but around 4" or 5" should be fine.
Most people use ordinary countersunk head screws, which will stick out a bit at the sides. A file can be the answer here, or if you can get domed (not round) head screws, so much the better. On my boat, a previous owner used ordinary countersunk brass screws, but skimmed the corners off the heads in a lathe. You may well think this is excessive, but if you have a lathe available, it doesn't take long to do a batch.
You MUST pre-drill the holes into the hull fairly accurately, and put in a steel screw of the same thread first, before inserting the brass one. Brass screws normally seem quite tough, but Sod's Law predicts you'll break one or two off if you don't put steel ones in first. Given that there will be a hundred or more to do, a cordless drill/driver with a variable torque limiter is very highly desirable. Sod's law also predicts that you'll strip the threads in the hull material for one or two screws: in that case I'd suggest cleaning out the hole and then pushing some epoxy putty into it. You can of course just put a larger screw in, but when the strip needs to come off temporarily in a few years time for painting or repairs, you'll curse having different sized screws!
Soldering the joints is not needed, and indeed may be worse than useless.
The hull surface behind the strip doesn't need to be completely flat, but you might like to go along with a file before starting to take any little lumps down. If you can get proper marine rubbing strip, it does have a somewhat concave back surface, and so will fit reasonably flush to gentle curves, but I wouldn't worry if your's is flat.
I wouldn't use any sealant or filler behind the strips unless the hull was very rough (cleaning it up is a pain), but if the deck gets varnished, a bit will trickle down into the crack behind the strip, and will do no harm