Are you sure about the KLM permitted size? They are quite generous and I'm sure they allow a bigger bag than Ryanair?
But if you are correct then it would probably be best to pay for a bag in the hold rather than buying 3 new hand bag cases?
People go on about doing hand luggage only but I don't think it's always worth it. We just did a hand baggage only holiday and had to spend most of the money saved on contact lens solutions, toiletries and suncream because of the liquids limit.
It's also loads extra hassle as you have to be really careful about what you take. I'd rather pay for a hold case unless only going for 2/3 days at absolute max and not worry so much about what I take and having to plastic bag minature toiletries.
I flew with KLM at the weekend. I actually thought their carry on luggage was generous. We checked bags anyway, but fwiw the crew told everyone whilst we were waiting to get on the plane that they were going to put all carry on cases in the hold anyway at no extra cost. The exceptions were those carrying medication and any bags that weren't suitcase shaped. The bags that were put in the hold last minute were brought out and left beside the plane when we disembarked so passengers didn't have to go through baggage reclaim.
The upshot of that very waffly paragraph is that I'd check in one bag rather than buy 3 new ones.