Hard to know how often someone may be ill. However adults usually have a better immune system than children, so fight off illness, plus may still be able to do some work whilst not feeling their best. Problems come though with long term illness, breaking bones - so whilst someone may not have any sick leave for many years, when they do need it it may be for weeks or even months.
Pros and cons to all types of childcare and parenting generally. You and DH need to have a good work life balance, spending time with your children - they quickly grow up, so look at what you can do... such as can you work from home, do 5 days work in 4 long days.
Once you have two or more children a nanny becomes more viable. The more children the better as nannies are paid per family, not per child. You dictate the salary so you can work out what you can afford, offer a bit below that and see what candidates you get.
You need to realise that you are a boss, an employer. That comes with various legal duties, including running payroll, paying Employers national insurance, having suitable insurance cover in case an employee injures themselves at your home, managing your employee, keeping track of holiday taken and agreeing holidays in advance. It all sounds a bit complex at first but you soon get into the swing of things and nanny payroll companies can take a lot of the burden off you for the financial related tasks.
How much a nanny will cost will vary a bit by area, city is often higher, especially London. There are some examples of cost of employing a nanny on here... have a look through past messages, use Advanced Search (if it's working) look for things like "Employers NI" as that will often pick out message threads to do with employing someone.