Keep it, burn it like Washington, or use it as a temporary base for the war? Was there much of a long term plan, or were they focused more on taking it first?
I've written pretty extensively before on the causes of the war, on British war aims and their alliance with American Indians, and how they contrasted with American goals. To make a long story short, the British were defending their colonies in Canada and the Caribbean from an American invasion, and they had no interest in conquering the United States, at any point in the war.
However, even in a purely defensive war, the British realized fairly quickly that passively defending their borders was not going to end the war quickly, and was unsuitable for the style of warfare preferred by their native allies - early, aggressive successes by British commanders like Isaac Brock earned the British a popular renown among American Indians, which contrasted heavily with Henry Procter. Brock was universally liked and respected by American Indians, and had a famous relationship with Tecumseh, who allegedly reported on meeting him: "This is a man!" Procter was likened to a bull, running away with its tail tucked between its legs.
But aggressive defense didn't necessarily mean that they were attempting to conquer the country, by any means. The goal was either to raid in such a devastating, sustained manner that the country would surrender or the civilian population would no longer support the effort (it was already highly unpopular), or to capture key cities and force a treaty on terms favorable to Great Britain. The (brief) capture of Washington was an effort to that end, and it should be noted that the destruction of public buildings was a recognized aspect of long 18th century warfare, and it was practiced on both sides. Burning the White House wasn't necessary and was viewed at the time as excessive, but it certainly wasn't beyond the pale, and Americans had done similarly in captured Canadian cities, as well.
By 1814, there were two large-scale efforts to end he war by capturing key cities. An invasion force assembled in Canada would sweep down into Northern New York, following Lake Champlain. A second force was being assembled in the Caribbean, and would invade the southern coast, capturing New Orleans. Of the two efforts, the New Orleans campaign was the more critical; New Orleans was an economic bottleneck, because it was where the Mississippi river met the sea, and a great deal of American agricultural produce was shipped down that river. With New Orleans in British hands, they would have a powerful bargaining chip with which to end the war.
Both of these campaigns ended in disaster, which gave a somewhat inflated impression to the American public that the war had been won when they heard news of the Treaty of Ghent following the battles of Platssburgh and New Orleans, more or less back-to-back.
The long term plan, such as it was, was end the war, hopefully from a position of strength. Being able to hand back an important city to the United States would be a powerful motivation to cave to British demands.
I'll be happy to answer follow-ups.
Jon Latimer's 1812: War with America and Donald Hickey's The War of 1812: A Forgotten Conflict are the two best overall histories of the war. For more on the American Indian role, check out John Sugden, Tecumseh's Last Stand