Sandy
Good plan - quite straightforward

Don't know if you have any access to old "comics", but Ricky Webb published many boats made of Styrene, with detailed instructions on each of them
Basically it goes like this:
Get styrene sheet - about 1.6mm thick (this is sold in HUGE sheets by plastics suppliers as HIPS sheet)
Cut templates in card - mark round on sheet and cut out (score about half the thickness and bend to snap sheet)
Assemble sheets together - I use pvc (insulating) tape; Ricky preferreed masking tape

Use one of the solvent cements applied with a small (cheap) paintbrush - the cement is so thin it will run into the joint
Leave overnight to harden

Remove tape and make sure all joints are glued (do not worry about any gaps)
Add Transoms, and any other internal bits

Add deck in similar way
GAPS - Ricky method - it has never really worked for me
put a puddle of solvent cement into an airtight jar (this is what the marmalade jars from hotel breakfasts are for

), add small bits of styrene offcuts, leave for an hour and adjust to creamy consistency
brush onto inside of seams and use to fill small gaps - put slices of styrene offcuts in and leave for an hour (top on!)
Adjust to milky consistency and brush into all joints (on the inside)
fill larger gaps with slivers of styrene

I used car body filler and squeezed a round fillet into all the seams
Ask if you need any specific help
andrew