Yes the gear will work, but do shop around a bit. Have a look at Component shop, Howes of Oxford, Marks model Bits. Shaving a few pounds off here and there will bring you nearer to your target figure. There are lower cost servos than the Futaba that work equally as effectively in a boat at much lower cost.
Unless you are determined to run on a LiPo, you dont need a Tio, the "ordinary" Marine Viper will do the job equally well.
Some of the items like the transmitter and the charger (dont stint on the charger, a good one will save a later fortune in batteries) will hopefully serve many years over hopefully many models, so thats a spread cost, even if its budget comes out of the same pocket as of now. One thing to watch for on modern radios is whether they are full range or "park flyer" types, which are only intended for close range operation.
For a displacement boat, a 545 might be more appropriate, Same size and mount, usually the same price.
Coupler bits, OK - yes it is a standard allen key, one of what will probably wind up being a collection of that size as they get lost, replaced and subsequently found as they come out of hiding.
On a single screw boat, handing doesn't matter. Terminology of handing varies between countries of origin anyway, some regarding rotation from the front of the boat looking back, others looking forward. Just make sure it is properly locknutted on helped with a bit of threadlock.
Most of my rudders were home made from brass rod, balsa laminations, plastic tube to match the rod and recovered bits from dead 13amp plugs, but commercial ones work well. Check the sizes against your plans, a big one costs more and might need a considerable amount cutting away at both ends. A small blade can be enlarged by sticking styrene sheet to it.
Over the years, I have noted that building a boat costs £100 plus £100 per foot length, as a rule of thumb. Lots of bought-in extras will obviously up the cost, home fabrication and more modest detail can reduce it.
As Ken said, read through the blogs, but use the search facility on the site as well. The browsing and reading will give lots of useful information