Some early-game thoughts:

Starting Position

Diplomatically, most of central and eastern Europe is friendly towards you, although these need to be handled with care. Diplomatic problems are likely in western Europe. The biggest single problem being France, which is a perfect storm of poor historic relations, powerful military, and proximity to your territories.

Militarily, Britain has the strongest navy, not least because it starts with a 2nd-tier Dockyard, so can produce 4th and 5th rate ship immediately. There are downsides. Those better ships cost more to make and maintain, yet your starting economy is not healthy. And while Britain is probably best placed to exploit the new world, there is always a danger of spreading yourself "too thin" by trying to cover too many different threates. The ever-present threat of war with France and tendency for European mainland wars to result in European piracy, almost forces you to keep a large navy close to England: A classic cold-war scenario, that ties up a lot of resources without resolution, but does maintain the European status-quo, allowing you to focus major military actions elsewhere.

There are 2 distinct types of region: Those that can build a wide range of capital buildings, and those that cannot. Ireland is restricted to basic colonial administration, in contrast to Edinburgh, which can build a wide range of capital buildings. The intuitive first move - to try and develop Ireland and benefit from it's large (3 million) population - has limited potential.

The population of Scotland and Ireland are in decline, while growth in England is very slow. Happiness is not high. At best this means you will not gain new sqaures within the region for development. At worst, you could see a rebellion. Long-term, this will mostly be addressed through research. Short term, consider dropping European lower-class tax slightly. Garrisoning units is not terribly effective, because the upkeep cost often outweighs tax benefit. Ireland is a particular problem, due to its high population, and lack of building potential.

Britain has a strong trading position, which initially is restricted by port capacity (check the reasons why there is no trade under Diplomacy). You cannot upgrade Greenwich without a lot of research. However, the next harbor to develop is Bristol, which can give England a second trading port. Push for anything that gives improved population growth in the first few turns (reduced tax, farms, related research).

The first tier of construction normally gives the most significant individual increase, as well as costing the least to build. So as a rule of thumb, always build on any empty squares before upgrading. England and Scotland start with 2 unused farm squares, so build on those immediately. There are also several unused squares in North America. In a few turns you can increase exports from North America by 3 or 4 times, simply by adding Fur trappers to Rupert's Land and a plantation in the Bahamas. That generates a lot of money!

Lastly, the first Prime Minister is a liability, and can easily be replaced at the start (you can kick one minister per turn).

Logical strategy

It will become apparent that there is more money to be made from trade than taxataion of the population. That shifts priorities away from European conquest, towards new world expansion. Plus the 13 Colonies mission and overall campaign objectives support that expansion. All topped off by the initial naval strength and ease of accessing the new world from Britain.

It is easy to get drawn into North America, since you start there. But don't leave India to late. It takes years just to travel there, is a campaign objective, and is exploited by other western Europeans.

It is inevitable that you will get caught up in European wars, but with a strong naval defense, I suspect there is no need to get embroiled in major conquests on the continent. It's important to get away from the "MTW mindset", that immediately propels Britain towards invading Europe, because that's the only place to expand.

Be careful not to get left behind: Technology and buildings all give exponential benefits. The further the game progresses, the harder it will be for you to catch up. Finding a balance between expansion/trade and the technology/build race is hard: A large geographic empire can easily fall because it is 10 years behind prevailing technology, or lacks sufficient buildings to support a powerful economy. Staying out of Europe (and so not being able to pilfer existing research facilities) can slow the pace of research, so be prepared to steal or trade research (particularly trade with those European nations that are not in the new world, so not likely to be fighting you).

Great Britain can do almost everything from its starting position, but that does not mean it should do everything! Focus on specific areas for territorial expansion, and coexist with everyone else as best you can.