The problem I see with your design is that the "one way vapor barrier" is a vapor barrier, but it's probably also a pretty effective water barrier. In this application, that vapor barrier is going to get cold. And gravity is not your friend, so the moisture that condenses on top of the cold vapor barrier is going to just sit there, becoming a mold/rot problem.
The simple rule is that you put the vapor barrier on the warm side of the insulation. In cold climates, that means to the inside. In warm climates, to the outside. Your profile indicates you're from the Czech Republic, so I'll suggest towards the inside for you.
As you add insulation, you can push this demarcation farther away from the edge. If you have enough insulation, you might be able to put the vapor barrier a few inches from the floor. This might be enough to let you change insulation types. For one example, you might use closed-cell spray foam and then batt insulation to fill the cavities. (This is popular in the southern USA, with the foam to the outside acting as a vapor barrier.) Changing insulation types can help you reduce costs - perhaps you want rock wool insulation facing the bottom, but you might choose to use just a single layer of that plus another layer or two of fiberglass or cellulose above it.
Almost any kind of insulation will be vulnerable to physical penetration by pests (nesting vs eating). You mention using "chicken wire" but most people's understanding of that product is small thin wires with a wide mesh, more than wide enough for mice and other small creatures to pass through. You might consider using a tighter wire product, such as lath mesh (which is steel with a small diamond pattern, used to secure stucco/cement to walls). Be aware that this can be costly - about USD$30 / 4x8 sheet-equivalent near me, versus about $8 for the same area of 1" chicken wire.
Finally, be aware that you need to particularly protect your joist bays from side penetration. It's easy to think about how you will keep vapor in/out of the bays relative to the floor, but think also about how the vapor will be kept out of the sides.