As usual this simple question gets stuck not on the correlation of forces but justification of why it would happen in the first place.
The British Empire decides that the USA is the main threat to itself than the Reich. This wouldn't actually be that hard; make Roosevelt et al more bellicose, while the Kaiser et al are more emollient towards London [after all, it could be said Berlin's biggest pre-war mistake was
forcing the UK into the Franco-Russian camp with a series of boneheaded moves.] Throw in other 'irritants' - from the American-Irish lobby to British suspicions that Washington is plotting to annex Canada and it's possible the situation could get
very bad very quickly.
Use Newfoundland and Victoria Island as staging areas. Declare some sort of friendly fleet action / wargame off the respective coasts. US will be interested but potentially blinded - have a series of invading forces already prepared along five axes.
From Montreal, head for Boston, New York, and ultimately DC.
From Niagara, head for Pittsburgh and Cleveland, then Columbus (if possible to also reinforce the New York/DC front).
From Windsor, hit Detroit then head for Toledo and Cleveland then Chicago
From Thunder Bay, head south to Minneapolis, Milwaukee & Green Bay, and ultimately Chicago.
From Sault Ste Marie, a largely brown water force to hit Chicago quickly and hold the city with the bulk of the force moving to control the Mississippi River. They also travel up the major branches of the river(s) to destroy bridges along with telegraph/telephone lines.
This first strike is not meant to take over the country, only assault and hold its major industrial centers, causing chaos while the Euro/World forces land supplemental forces largely into the Northeastern US. Command and Control likely falls back to Denver or Salt Lake City, with a largely partisan affair in the Occupied Territories which initially are contained to those areas north of the Ohio and east of the Mississippi. If the brown water force fails early it makes the entire plan all the more risky. Even with DC in Euro/World hands, the US is going to fight on - and there will be a lot of very angry folks in the Northeast willing and able to assist in their own liberation as well.
That looks rather like
War Plan Red. But I disagree with the main assumption - that the war would
start in North America.
The USA in 1914 has more commitments than simply the continental US. There's the Pacific Islands [including Hawaii], the Philippines, Alaska, the Panama Canal, Puerto Rico, the Virgin Islands and the forces within Cuba and I
think Haiti.
In Washington's case, while it may
like to invade Canada it will surely be intimidated by the sheer geographic size. They may also may feel the need to station forces on the Mexican border to deter any 'adventures'. They need to buy
time; not just to conscript men and make matériel, but to
design the matériel to make and to train a large amount of NCOs and junior officers to make this army competent.
In this case, the Americans may decide that the Philippines and
possibly Alaska are indefensible. Any 'extra' forces [if there is any] must go into defending the Caribbean, especially the Canal.
On the European side, an attack on the Philippines will be the first major one; it's close enough to their holdings to use 'colonial' troops. This will be easier if the American's don't try to rush reinforcements to it. I think it's reasonable enough to assume it will either fall or at least be 'neutralised'. Then what?
The British – the unofficial leaders of the alliance – will first of all worry about Canada. More than anything else, they'll desire to keep Halifax and Vancouver as bases, and ideally also hold onto the Canadian 'industrial core' which is a rough triangle between Quebec - Toronto – Thunder Bay. They'll primarily worry about the USN being able to blockade said Canadian bases [which will be critical for any 'American Invasion']. I suspect the RN will get very interested
very quickly in either blocking or perhaps even capturing the Panama Canal; if the Americans lose this, the USN will be cut in half.
The next phase all depends on the general 'war aims' of each side. I'll tentatively suggest that for the Americans, they'd like to see a) Canada merged into the USA b) Bermuda annexed, c) enemy acceptance of the Monroe Doctrine and - if possible - d) the transfer of various Pacific/Caribbean Islands to US jurisdiction. For the Europeans it will - I suspect - be the complete shearing-off of all American holdings past the continental USA. There would also be issues for 'indemnity payments' due to the almost-certain seizure of the billions of assets, debt etc by Washington [In RL, British investment in the USA in 1914 was $7 billion alone]. Direct conquest of American states I suspect won't be on the table, believing that it will simply be 'more bother than they're worth' - but I could see them trying to exploit divisions, such as seeing if succession by neo-Confederates / New England / California / Utah etc is possible.