Prince William and Kate Middleton have been holding discussions over the royal wedding, which is due to take place in London next spring or summer.
A spokesman for St James's Palace said the couple were "still on cloud nine" after announcing the engagement.
The palace confirmed Westminster Abbey was among the wedding venues under consideration after Miss Middleton was photographed there on Wednesday night.
Meanwhile, Sir Tom Jones has offered to sing at the ceremony.
And US President Barack Obama said he "sends best wishes" to the couple, according to a White House spokesman.
The news of the engagement triggered congratulations and widespread news coverage around the world.
The St James's Palace spokesman said: "They are still very much on cloud nine and are still enjoying the happy moment.
"They are enjoying talking to friends and family and enjoying one another's company and showing their commitment to each other publicly."
He said "all options are on the table" after the couple spent part of Wednesday discussing options with officials.
Miss Middleton visited the abbey in the evening with aides after it was closed early for the private visit.
Prince William was unable to make the trip as he had returned to North Wales to continue his RAF work.
A St James's Palace spokesman said: "Miss Middleton paid a short, private visit to Westminster Abbey in order to be able to consider it as an option."
Aides will now consult with the Queen, senior royals, Miss Middleton's parents and others before reporting back to Prince William and Kate, who will make the final decision.
The spokesman stressed the prince, who is second in line to the throne, and his bride-to-be were conscious of the country's economic situation.
Speculation has also focused on St Paul's Cathedral and the smaller Guards Chapel, where the 10th anniversary memorial service for Princess Diana's death took place, as other possible venues.
The couple will live in North Wales following the event. The spokesman added that Miss Middleton will also give up her job working for her parents' business Party Pieces, once she joins the Royal Family.
Meanwhile, a group of schoolchildren from Westminster's St Augustine's primary school discussed the wedding with the Duchess of Cornwall as they rode a Routemaster bus through the centre of London.
She told them it would be a "big wedding" and they will "even invite the Queen", some of the children said afterwards.
'Excitement and anticipation'
In the Commons, Prime Minister David Cameron made a statement to MPs: "I'm sure the whole House will wish to join me in sending our warmest congratulations and best wishes to Prince William and Kate Middleton on their engagement.
"I'm sure everyone agrees this is wonderful news, we look forward to the wedding itself with excitement and anticipation."
Speaking about his offer to perform at the wedding ceremony, Sir Tom Jones said he had "always been a royalist and I always will be.
"If they invite me along to the wedding I'd happily come and sing a few songs."
BBC royal correspondent Nicholas Witchell said Buckingham Palace would be "very sensitive" to the economic climate when making its plans.
He said: "They will want to send a very definite signal that it is not on the lavish scale of the Charles and Diana wedding of 30 years ago, that it will be a royal wedding suitable and appropriate to the times."
Anti-monarchy group Republic said taxpayers should not have to pay any money towards the event as the wedding should be "private".
But the chief executive of VisitBritain, Sandy Dawe, said the wedding would be a great tourist attraction.
"We've seen the story of their announcement of the marriage go global. The ceremony itself could attract many billions of viewers around the world and that publicity is almost bound to generate more visitors from overseas."
Speaking in a joint television interview, the prince said he gave his fiance his mother Diana's engagement ring, having carried it in a rucksack for three weeks.
"It's my mother's engagement ring so I thought it was quite nice because obviously she's not going to be around to share any of the fun and excitement of it all - this was my way of keeping her close to it all," he said.
His bride-to-be called the late princess "an inspirational woman" and said that joining the Royal Family was a "daunting prospect" but something she hoped to take in her stride.