This is one subject that I can definately provide you with lots of information on. Other than wargaming I am also involved in 18th century re-enactment and have spent a lot of time researching historically correct clothing for sailors in the 18th century.
The short answer to your question is that the Royal Navy had NO uniforms during the first half of the 18th century. Marines at the start of this period had army uniforms (red coats with mitred hats), but they were actually from ARMY regiments designated for sea service and were disbanded at the end of the war of Spanish Succession and not reformed until the late 1730's/ early 1740's when Britain went to war again with Spain.
Navy officers typically wore gentleman's travelling clothing (frock coat, cocked hat, etc.) in their own choice of colour, although red was popular (being a 'military' colour). The only distinction that he was an officer would be the wearing of gold braid round his hat and, during the reigns of various King Georges, a black cockade on the front of the hat above the left eye. Officers would typically wear a gentleman's small sword for formal occasions or if on land and not expecting trouble. For a fight most officers chose a heavier blade (a boarding curlass, cavalry sword or a short hunting sword) and a couple of pistols for good measure.
Ordinary sailors wore practical seamen's clothing. Although not uniformed, there was a degree of unifirmity to their dress due to the bulk purchase of slop clothing sold to the sailors from the ship's 'slops chest'. In the period up to 1730 this would include short GREY coats (not blue coats - these only appeared after 1748 when officers got proper uniforms), red waistsoats and red breeches. Other colours were worn too - if you volunteered or were pressed and had your own grey/green/blue/brown sailor's coat, waistcoat or breeches you would not be expected to purchase a new one from the slops chest.
In summer or in warmer climates sailors would wear long baggy 'slop' trousers of varying lengths (from just below the knee to above the ankle). These were made by the sailors themselves and were typically made from lightweight hemp/linen canvas which would fade to a pale grey/brown 'oyster' colour. In winter knee breeches were worn, typically with a knee-length canvas overskirt that could be tarred. Shoes were not worn onboard ship. Hats could include knitted 'monmouth' hats (close-fitting knitted hats), felt hats (by the 1730's these could be tricorn types, often with very narrow brims) or (for Scottish sailors) blue Scots bonnets.
Midshipmen, although only typically 12 to 18 years old, would normally dress as ordinary sailors, but if on duty (e.g. commanding a watch onboard ship) would usually be expected to dress "as befits a quarterdeck officer".
Weapons for sailors would include cutlasses (with black iron figure-of-eight guards), boarding axes, boarding pikes(only of involved in a boarding action), pistols, muskets and the dreaded blunderbus (with brass barrels often 16" / 40cm or less in length).
I don't have any pictures available to post at the moment (I will try to sort that out tonight).
Catwoman - I see you are in Ringwood. I only live in Poole so please feel free to contact me off-board if you have any questions or want me to send you more information.