Health is paramount. Don't adopt a second cat until it has been cleared by your vet as healthy. You already lost one, you don't want to loose another.
In term of age, adult cats get along better with young cats who are not mature enough to be seen as rivals. The youngest age you should consider is about six to eight weeks. Until then, they need their mum's milk (or if you don't mind feeding from your tits).
Unless your cat is very friendly and social able, pick a young cat aged eight months or below as your kitty companion. Most cats make friends in about one or two weeks. some may even take a month. The most important thing is to foster the friendship is not to interfere too much but make sure that your cat knows that it is the favorite. It just lost a companion, it need all the support although there is a new one in the family.