In 1562, Elizabeth Tudor had been Queen of England for just four years. She contracted smallpox. It was thought by almost everyone she was going to die and provoked a massive succession crises in her council. There were several cadidates, some more practical than others, some more powerful than others, some favoured by the people, some by the council, some by neither!
The Primary Candidates1. Lady Katherine Grey - Katherine was the most likely cadidate. Under the terms of Henry VIII's will, she stood to inherit the throne after Elizabeth. She was a Protestant, which found favour with most English people. The Council saw that here was a well educated but rather stupid woman whom men like William Cecil could have manipulated easily. But there were some disadvantages to Katherine's candidature - namely, she was at the time in the Tower for contracting an illegal marriage to Edward Seymour, Earl of Hertford. So, if she was accepted as heiress presumptive, the councillors would have been obliged to release 'Queen Katherine' from the Tower. Also, though she was married, the legitimacy of her marriage was in doubt - in fact, it had been declared null and void by Elizabeth. No doubt as queen, Katherine would have been able to find clerics to declare her marriage valid, but what if one day, her son, as 'Edward VII' would be confronted with the question of his legitimacy? It could end in civil war.
2. Mary Stuart, Queen of Scots - Mary was something of a dark horse. Technically, she had the most superior claim, ad she was in the senior line of descent from Henry VII. Also, she would have the backing of not just Scotland, but perhaps of France also. She was a Catholic, but a French army might have been able to force the English to accept her. She was young, and able to bear children as far as was known. However, there were several points against her - Margaret Tudor had renounced the dynastic claims of any descendants of her marriage to James IV: this obviously included Mary, though it is doubtful that anyone recalled this in 1562. Also, Philip II of Spain would resist her enthronment, to counter act the French influence. Also, as a Catholic, she would be deeply unpopular with her subjects.
3. Margaret, Countess of Lennox - Lady Margaret was 47 in 1562, married with two sons. She was a Catholic, which counted against her, but, she could also claim to have a better right to the throne than both Katherine and Mary - Katherine by seniority and Mary because Margaret, unlike her niece, had been born in England, and Margaret Tudor's renounciation had not counted towards the issue of any subsequent marriage. She was also married to a potential claimant to the Scottish throne, and the mother of two healthy sons, which was a definite point in her favour.
4. Henry Stewart, Lord Darnley - It was certainly possible that Margaret Lennox, like her ancestor Margaret Beaufort, would choose to renounce her rights in favour of her son, Henry. Darnley was young, handsome and well known at the English court. That said, he was also a Catholic - was a Catholic king any more acceptable than a Catholic queen? Through his father, he had a potential claim on the Scottish throne.
5. Charles Stewart - Darnley's brother. Would not be considered while Darnley was alive.
6. Lady Mary Grey - Katherine's sister. Would not be considered while Katherine lived.
7. Margaret, Lady Strange - a rank outsider, the daughter of Eleanor Brandon. I'm not sure whether she was Catholic or Protestant at this time - anyone know? She was 22, married to Henry Stanley, Lord Strange, heir to the Earl of Derby, and the mother of two young sons - Ferdinando and William. If she was Protestant at this time, and Margaret Tudor's descendants were to be ruled out because of their Catholocism, and Katherine Grey because of her dubious marriage, then Lady Strange was a definite possibility.
The Secondary CandidatesThere was even talk at this time of not bothering with the Tudor descendants, and placing a Plantagenet on the throne. These names were bandied around the Privy Council at the time.
1. Henry Hastings, Earl of Huntingdon - he was descended from George, Duke of Clarence through the latter's daughter Lady Salisbury. He was a Protestant, but had no real wish to be King of England. He was married to Robert Dudley's sister, Katherine.
2. Henry Manners, Earl of Rutland - he was descended from Edward IV's sister Anne. He was married to Margaret Nevill, who had Plantagenet blood too - she was descended from Henry IV's sister Elizabeth.
3. Henry Nevill, Earl of Westmorland - the brother of Margaret, Lady Rutland, who had a claim through Henry IV's sister Elizabeth.
4. Foreign claimants - to acknowlege the claims of the Nevills, though, also meant acknowleging that of others with Lancastrian descent - including Philip II of Spain and Joao I of Portugal. I think we can safely say neither of these men stood a chance of becoming king of England in their own right!

5. Thomas Howard, Duke of Norfolk - not so much as an outsider as he seems at first. Norfolk was young, married, and had a son. He also had Plantagenet blood through his grandmother Elizabeth Stafford, and was the premier peer of the realm - but a Catholic.
Any comments on this? Who would you have chosen?