With Ryan Air, and any budget airline in Europe, my advice is the same. Do not worry so much about size, it will be the weight that gets you and the number of items you wish to bring.
In the US, we seem to ignore carryon weight, if it crams through the xray, it is fine, then also bring a daypack, a purse, or carry a shopping bag.
Europe is different. For RyanAir, the checked item has to be of the size stated, but you also need to be under 22 lbs, tough to do for a multi country trip, especially if you pick up a few things along the way. You can also have an item of "hand baggage", but this is not a daypack, but a small purse or other similar item.
As for enforcement, my experience is that in the UK, Ireland, and Germany, it is strictly enforced, either before security or at the gate. The further South, enforcement is less strict. I would not count on this, and other's experience was likely different.
So what to do? Find a bag that works for you and holds the things you need, plus some spare room for souvenirs. If it is larger than the requirements and fully packed (with your daypack inside) is over 15 pounds, then just plan on paying for a checked bag! They are not trying to rip you off, they are offering those that can live with the strict limits and booking far in advance a dirt cheap ticket. For you as a tourist, paying for a bag is typical, and you are still getting a dirt cheap ticket with the baggage cost, why risk it?