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You need an Armory to build Artillery and a Shipyard for ships.

Wagon Train 39 hammers
Artillery 192 hammers, 40 tools, Armory
Caravel 128 hammers, 40 tools, Shipyard
Merchantman 192 hammers, 80 tools, Shipyard
Galleon 320 hammers, 100 tools, Shipyard
Privateer 256 hammers, 120 tools, Shipyard
Frigate 512 hammers, 200 tools, Shipyard

Costs in Europe:

Artillery 500 gold + 100 gold for each Artillery you've bought
Caravel 1000 gold
Merchantman 2000 gold
Galleon 3000 gold
Privateer 2000 gold
Frigate 5000 gold

Initially the cost of Artillery in Europe is much lower than that for ships, but it gradually rises. In the colonies Artillery is relatively expensive to build compared to ships.

I used to think that fortresses full of Artillery were the way to fight the Royal Navy, but I was thinking in terms of early European prices (Artillery for 500-1000 gold, Frigate for 5000 gold), and assumed that colony prices have similar (10:1 - 5:1) proportions. They happen not to, and a Frigate costs about as much as 3 units of Artillery (8:3 in term of hammers, 5:1 in terms of tools).

A Frigate attacking a Man o'War has a reasonable 50% chance of winning (16+50% attack bonus strength against plain 24) and is mobile, so it can protect a few colonies.

A lot of Artillery in a Fortress has higher firepower, doesn't get damaged in case of a defeat against ships and protects against land attacks as much as against naval attacks, but you need to build those Fortresses everywhere (or at least Forts), and you need a lot of Artillery in every coastal colony, because it's extremely immobile (only 3 squares per turn on roads, and it's very vulnerable in travel - use a Privateer or some other ship to transport them if you can).

Making Artillery is still probably a better idea than building Frigates, but not by as big margins as I once thought.

Building Galleons and Privateers is a good idea, unless all your Carpenters are too busy with their buildings (during development of industry you need so many buildings that you're very likely to have too few Carpenters).