If you're going to all three of the "Big 3," buy the combo ticket, which allows you to skip the ticket buyers lines and saves some money. It's called the Paseo del Arte ticket.
You can buy it at any of the museums; if you're going before the crowds get bad at the Reina Sofia or the Thyssen, or going later in the day to the Prado (after the worst ticket lines have dissipated) you won't have a long wait to buy it.
The Prado's ticket website is down. But the Reina Sofia's site says the following:
The Paseo del Arte Ticket must be redeemed at the ticket offices of the museum where the online purchase was made.
Tickets purchased through the Museo Reina Sofía website must be redeemed at the Reina Sofía’s Express Ticket Offices.
Once the ticket has been redeemed, the three museums can be visited in any order. The museums can be accessed directly, without passing through the ticket offices.
The price of the ticket includes a 20% discount on the current admission prices in the three museums.
The Thyssen's website has similar language; a Paseo del Arte bought from them must be redeemed at their "priority ticket office," but then can be used in any order, for one visit to each museum's permanent collection (special exhibits are extra).
Presumably these special ticket offices have shorter lines than the general admission ticket windows.
So, if you're really worried, buy the Paseo del Arte ticket from the website of the museum you will visit first. I recommend visiting the Prado last, because any other museum is second tier after the Prado.
Here's the link to buy it from the Thyssen: https://entradas.museothyssen.org/selection/pass?productId=447882985
and from the Reina Sofia: http://www.museoreinasofia.es/en/visit/buy-tickets/paseo-arte-ticket