I play England/GBR almost exclusively thus far (I really do need to branch out sometime!)
Here are my thoughts, based on what I've done.
I would take a Diplomatic group first.
Exploration will allow you to get Quest for the New World, and quickly reveal TI, and get the choice picks for colonisation. It's also very handy being able to reveal TI for yourself, going wherever you want. And it boosts Prestige by +1 for each province revealed, making it easy to keep at or near 100.
It's obviously geared to Colonisation, and it's good for that. Besides that, it's a bit meh.
The bonus is pointless - you really don't need a free CB against Pagans; just put a colony next to them, Fabricate, Full Annex. The AE doesn't matter in the New World.
(Maybe this will change in 1.4/CoP.)
Expansion is a much nicer Diplomatic set overall, and a great first choice.
You still get a Colonist, and also an extra Merchant. Extra Diplomatic Reputation, extra Diplomatic Relations, boosted Trade, and an Asian expansion CB as the bonus.
In my first England/GB game, I took Exploration. In my second, I took Expansion. Not being able to reveal TI has been a regular annoyance, but never more than minor. It really has not significantly hampered my colonisation efforts at all. It meant that my first New World colony and annexations happened in 1551, instead of 1490 or so. But I still got all the colonies I wanted, I still annexed all of the New World nations, I still totally dominated Chesapeake trade node.
And I now have a far, far stronger Diplomatic game. I've had up to 11 vassals/PU-minors, and the DipRel and DipRep were vital here. The extra merchant has helped enormously with trade income. The bonus CB is going to be very useful when I push into Asia, which I didn't do at all in my first game.
So this one is down to your taste, but you certainly don't have to take Exploration in order to colonise/expand well, and I would strongly consider Expansion if you're OK with the annoyance of waiting for TI and sometimes not being able to go exactly where you want. Note that once you DOW a nation, you can then reveal all its territory; I used this for example to reveal all Sub-Saharan Africa, as soon as I could see one province of Mali.
I wouldn't take
Diplomatic first - as you see below, I like it for my fourth group; but I don't feel it's as strong for an opening idea, because getting an extra Merchant and Colonist early is very helpful.
That said, I could see an argument for taking something else first, and Expansion second, on the basis that the Merchant and Colonist are not so valuable before 1500, and something else might be.
So I could well see an argument for swapping my first and second proposed Ideas - taking Military first so you immediately have 25% Morale and can kick ass in early game; then take Expansion a little later when you can use the Colonist and better use the Merchant, and are now starting to get more hampered by reduced DipRel and Rep and so on.
Second group, Military
I took Defensive second for that 25% Morale. Morale is King. The Army Tradition is also very helpful, as is reducing Maintenance.
This is a very good general purpose strategy. It's maybe slightly less relevant for England-with-France, because you have the French army on your side. But still, in the first 100 years of the game, it's not going to be certain that you can easily beat Burgundy + Austria + others if they do come fight you. And Burgundy have always hated me, especially when I pushed into Antwerpen. So Morale is hard to argue against.
I took this group second, and I think it will be the only Military group I ever take, as I now have both Spain and Portugal as PU minors, and they (well, mostly Spain) basically win all my wars for me anyway. But I feel that if I'd not even taken this, I'd have been constantly worried about morale at least in the early game. And I might have struggled to even get Spain in the PU, as it required beating both Spain and Portugal with 84% WS, with only Austria as a (nearly useless militarily) ally.
Third, I took Administrative
I wanted to take an Admin idea before I took another Diplomatic, as I was regularly short of Dip points and I wanted one of each group.
I took
Administrative mostly for the Merc benefits. My thought process was that I wanted to be able to war regularly, and not have to wait for Manpower recovery. I expected to have quite a bit of money - and indeed I do; now in 1600 I make +100 a month - and so spamming Mercs is very helpful. But you need more of them, and if you want them to be a total Manpower replacement, you don't want the costs to cripple you, even if you do have quite a bit of money.
The -25% core creation cost I've also enjoyed. I have been Vassal Feeding extensively in this game, following my heavily Diplomatic strategy. But I still I cored the entire New World myself, because it's already heavily discounted, and I didn't want to have any vassals over there because of the various advantages to annexing. So that extra 25% certainly saved a few hundred admin points. I also ended up coring parts of Burgundy, such as Antwerpen and Breda, which were HRE territory and I couldn't vassal-feed.
+1 Advisors is always generally helpful. When you need a specific advisor, you'll be thankful for an increased chance of getting him. I'm thinking specifically of the +5 DipRep guy, whom I always want when I am annexing/integrating.
I guess this group has had a lower impact on my game than the others so far. Then again, I have spammed Mercs heavily, and in recent wars they have been 80+% of my army, and I've been able to fight, fight and fight again when otherwise I'd have been waiting for Manpower regeneration. So it has been useful, if not decisive.
Fourth, I took Diplomatic
I really wanted to push the Diplomatic game, so this was my natural next choice. That extra Diplomat I really rely on, even though I already had +1 from Embassy, +1 from Curia Controller. I've never had enough Diplomats in this game, I am constantly using all of them (even now, in 1600, when I have 6 total.)
-50% Fabricate Claim is great because I want to war often, and it's not only quicker, it's half the chance of discovery and extra AE.
Rev/Counter-Rev CB: awesome; more war opportunities, even though I'm a Monarchy. And it gives me the chance to choose to change to a Republic if I want, and then I'd get
dozens of CBs.
Diplomatic Relations, vital. I not only had up to 11 subject nations, I was also regularly Allying with nations to greatly reduce AE. I've had up to 15 Diplomatic Upkeep at various times, still losing Dip Points even with my current limit of 12 DipRel.
Dip Reputation speaks for itself, can't do without it. Annexing vassal time is so much reduced with +15 DipRep as I have now. Not to mention the chance to diplo-vassalise some much bigger nations. I can currently dip-vassalise Norway, which is the most impressive I've personally had thus far.
That takes me up to the present in my current GBR game. I haven't quite decided what to do with my fifth group, but
Trade is a strong possibility. I already have +60 income from 3 merchants, I really want to see what I can do with 6!
My key feedback is that the Diplomatic game is hugely powerful, and I am really glad I emphasised it.
I am now completely unstoppable, especially now I'm also HRE Emperor. Again, Diplomacy helped hugely there: I took four vassals purely for Elector Voting purposes. I'd have had 0 Dip Points forever if I'd not strongly emphasised DipRel, and I'd be stuck with those vassals a lot longer if I'd not got as much DipRep as possible. (Of course, getting HRE Emperor helped even more with all of this - boosting Rep, Rel, and giving me another Diplomat. I have 6 now and it's lovely

)